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@inproceedings{vismey10,
	Abstract = {These Proceedings contain papers that were presented at the Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing which was held at Allerton House, Monticello, Illinois, on September 29-October 1, 2010. As in past years, the Conference was sponsored by the Coordinated Science Laboratory and the Department of Electrical and Computer Engineering of the University of Illinois at Urbana-Champaign.},
	Author = {Viswanath, P. and Meyn, S.},
	Booktitle = {Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on},
	Date-Added = {2011-04-01 12:36:59 -0500},
	Date-Modified = {2011-04-01 12:36:59 -0500},
	Doi = {10.1109/ALLERTON.2010.5706875},
	Pages = {1},
	Title = {Foreword},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ALLERTON.2010.5706875}}

@inproceedings{sadmoumey10,
	Abstract = {This paper proposes new tools for steganalysis of queue-based stegocodes over covert timing channels. We study a universal estimator for the Kullback-Leibler (KL) divergence rate between the covertext process and the stegotext process. We empirically illustrate the performance of our estimator on some simple queue-based stegocodes and study its convergence properties.},
	Author = {Sadasivam, S. and Moulin, P. and Meyn, S.},
	Booktitle = {2010 IEEE International Workshop on Information Forensics and Security (WIFS)},
	Date-Added = {2011-04-01 12:36:16 -0500},
	Date-Modified = {2011-04-01 12:36:16 -0500},
	Doi = {10.1109/WIFS.2010.5711459},
	Keywords = {Kullback-Leibler divergence rate;queue-based stegocodes;steganalysis;stegotext process;timing channels;universal divergence-rate estimator;codes;steganography;},
	Month = dec.,
	Pages = {1 -6},
	Title = {A universal divergence-rate estimator for steganalysis in timing channels},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/WIFS.2010.5711459}}

@article{mil10,
	Author = {Milenkovic, O. and Alterovitz, G. and Battail, G. and Coleman, T. P. and Hagenauer, J. and Meyn, S. P. and Price, N. and Ramoni, M. F. and Shmulevich, I. and Szpankowski, W.},
	Date-Added = {2011-04-01 12:31:32 -0500},
	Date-Modified = {2011-04-01 12:31:33 -0500},
	Doi = {10.1109/TIT.2009.2036971},
	Issn = {0018-9448},
	Journal = TIT,
	Month = feb.,
	Number = {2},
	Pages = {649 -652},
	Title = {Introduction to the Special Issue on Information Theory in Molecular Biology and Neuroscience},
	Volume = {56},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TIT.2009.2036971}}

@inproceedings{beryu10,
	Abstract = {We consider the classical finite-state discounted Markovian decision problem, and we introduce a new policy iteration-like algorithm for finding the optimal Q-factors. Instead of policy evaluation by solving a linear system of equations, our algorithm involves (possibly inexact) solution of an optimal stopping problem. This problem can be solved with simple Q-learning iterations, in the case where a lookup table representation is used; it can also be solved with the Q-learning algorithm of Tsitsiklis and Van Roy [TsV99], in the case where feature-based Q-factor approximations are used. In exact/lookup table representation form, our algorithm admits asynchronous and stochastic iterative implementations, in the spirit of asynchronous/modified policy iteration, with lower overhead advantages over existing Q-learning schemes. Furthermore, for large-scale problems, where linear basis function approximations and simulation-based temporal difference implementations are used, our algorithm resolves effectively the inherent difficulties of existing schemes due to inadequate exploration.},
	Author = {Bertsekas, Dimitri P. and Yu, Huizhen},
	Booktitle = {Decision and Control (CDC), 2010 49th IEEE Conference on},
	Date-Added = {2011-03-12 18:38:36 -0600},
	Date-Modified = {2011-03-12 18:38:36 -0600},
	Doi = {10.1109/CDC.2010.5717930},
	Issn = {0743-1546},
	Note = {LIDS report 2831, M.I.T., April 2010; revised October 2010. (Also, Technical report C-2010-10, Dept. Computer Science, Univ. of Helsinki.)},
	Pages = {1409 -1416},
	Title = {Q-learning and enhanced policy iteration in discounted dynamic programming},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2010.5717930}}

@article{van09a,
	Author = {van Handel, Ramon},
	Coden = {APBYAE},
	Date-Added = {2011-03-12 09:30:55 -0600},
	Date-Modified = {2011-03-12 09:30:55 -0600},
	Doi = {10.1214/08-AOP448},
	Fjournal = {The Annals of Probability},
	Issn = {0091-1798},
	Journal = {Ann. Probab.},
	Mrclass = {60J05 (60K37 62M20 93E11 93E15)},
	Mrnumber = {2561436 (2011a:60256)},
	Mrreviewer = {Abhay G. Bhatt},
	Number = {5},
	Pages = {1876--1925},
	Title = {The stability of conditional {M}arkov processes and {M}arkov chains in random environments},
	Url = {http://dx.doi.org/10.1214/08-AOP448},
	Volume = {37},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1214/08-AOP448}}

@article{van10a,
	Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	Adsurl = {http://adsabs.harvard.edu/abs/2010arXiv1009.0507V},
	Archiveprefix = {arXiv},
	Author = {van Handel, Ramon},
	Date-Added = {2011-03-12 09:30:35 -0600},
	Date-Modified = {2011-03-12 09:31:37 -0600},
	Eprint = {1009.0507},
	Journal = {ArXiv e-prints},
	Keywords = {Mathematics - Probability, Mathematics - Dynamical Systems, 37A25, 37A50, 60F20, 60G35, 60J05, 60K37},
	Month = sep,
	Primaryclass = {math.PR},
	Title = {A nasty filtering problem},
	Year = 2010}

@article{unnveemey11,
	Author = {Unnikrishnan, J. and Veeravalli, V. V. and Meyn, S.},
	Date-Added = {2011-03-11 15:27:31 -0600},
	Date-Modified = {2011-03-11 15:31:46 -0600},
	Doi = {10.1109/TIT.2011.2104993},
	Issn = {0018-9448},
	Journal = TIT,
	Number = {3},
	Pages = {1604 -1614},
	Title = {Minimax Robust Quickest Change Detection},
	Volume = {57},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TIT.2011.2104993}}

@article{huaunnmeyveesur11,
	Abstract = {For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal test statistic can be written in terms of Kullback #x2013;Leibler (K-L) divergence between the empirical distribution of the observations and the null hypothesis distribution. In this paper a modification of Hoeffding's test is considered based on a relaxation of the K-L divergence, referred to as the mismatched divergence. The resulting mismatched test is shown to be a generalized likelihood-ratio test (GLRT) for the case where the alternate distribution lies in a parametric family of distributions characterized by a finite-dimensional parameter, i.e., it is a solution to the corresponding composite hypothesis testing problem. For certain choices of the alternate distribution, it is shown that both the Hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents. A consequence of this result is that the GLRT is optimal in differentiating a particular distribution from others in an exponential family. It is also shown that the mismatched test has a significant advantage over the Hoeffding test in terms of finite sample size performance for applications involving large alphabet distributions. This advantage is due to the difference in the asymptotic variances of the two test statistics under the null hypothesis.},
	Author = {Unnikrishnan, J. and Huang, D. and Meyn, S. P. and Surana, A. and Veeravalli, V. V.},
	Date-Added = {2011-03-11 11:52:15 -0600},
	Date-Modified = {2011-03-11 11:52:15 -0600},
	Doi = {10.1109/TIT.2011.2104670},
	Issn = {0018-9448},
	Journal = TIT,
	Number = {3},
	Pages = {1587 -1603},
	Title = {Universal and Composite Hypothesis Testing via Mismatched Divergence},
	Volume = {57},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TIT.2011.2104670}}

@inproceedings{meycheone10,
	Abstract = {We present an on-line crosslayer control technique to obtain policies for wireless networks. Our approach combines network utility maximization and adaptive modulation over an infinite discrete-time horizon using a class of performance measures we call ime smoothed utility functions. We model the system as an average-cost Markov decision problem. Model approximations are used to find suitable basis functions for application of least squares TD-learning techniques. The approach yields network control policies that learn the underlying characteristics of the random wireless channel and that approximately optimize network performance.},
	Author = {Meyn, Sean and Chen, Wei and O'Neill, Daniel},
	Booktitle = CDC2010,
	Date-Added = {2011-03-07 14:08:42 -0600},
	Date-Modified = {2011-03-07 14:08:52 -0600},
	Doi = {10.1109/CDC.2010.5717192},
	Issn = {0743-1546},
	Pages = {1951 -1956},
	Title = {Optimal cross-layer wireless control policies using TD learning},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2010.5717192}}

@inproceedings{yinmehmeysha10b,
	Abstract = {This research concerns a noncooperative dynamic game with large number of oscillators. The states are interpreted as the phase angles for a collection of non-homogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto.},
	Author = {Yin, Huibing and Mehta, Prashant G. and Meyn, Sean P. and Shanbhag, Uday V.},
	Booktitle = CDC2010,
	Date-Added = {2011-03-07 14:08:42 -0600},
	Date-Modified = {2011-03-07 14:08:57 -0600},
	Doi = {10.1109/CDC.2010.5717142},
	Issn = {0743-1546},
	Pages = {3125 -3132},
	Title = {Learning in mean-field oscillator games},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2010.5717142}}

@book{kal80,
	Address = {New York},
	Author = {Kallianpur, Gopinath},
	Date-Added = {2011-03-05 18:27:54 -0600},
	Date-Modified = {2011-03-05 18:27:54 -0600},
	Isbn = {0-387-90445-X},
	Mrclass = {60G35 (60Gxx 60Hxx 60J65 93E11)},
	Mrnumber = {583435 (82f:60089)},
	Mrreviewer = {B. L. Rozovski{\u\i}},
	Pages = {xvi+316},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics},
	Title = {Stochastic filtering theory},
	Volume = {13},
	Year = {1980}}

@book{lipshi01,
	Address = {Berlin},
	Author = {Liptser, Robert S. and Shiryaev, Albert N.},
	Date-Added = {2011-03-05 18:27:54 -0600},
	Date-Modified = {2011-03-05 18:27:54 -0600},
	Edition = {expanded},
	Isbn = {3-540-63928-4},
	Mrclass = {60-02 (60G35 62-02 62L10 62Mxx 93Exx)},
	Mrnumber = {1800858 (2001k:60001b)},
	Note = {Applications, Translated from the 1974 Russian original by A. B. Aries, Stochastic Modelling and Applied Probability},
	Pages = {xvi+402},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Statistics of random processes. {II}},
	Volume = {6},
	Year = {2001}}

@book{kus77,
	Address = {New York},
	Author = {Kushner, Harold J.},
	Date-Added = {2011-03-05 18:27:54 -0600},
	Date-Modified = {2011-03-05 18:27:54 -0600},
	Mrclass = {93E25 (65N10 60J60)},
	Mrnumber = {0469468 (57 \#9258)},
	Mrreviewer = {Jean-Michel Bismut},
	Note = {Mathematics in Science and Engineering, Vol. 129},
	Pages = {xvii+243},
	Publisher = {Academic Press [Harcourt Brace Jovanovich Publishers]},
	Title = {Probability methods for approximations in stochastic control and for elliptic equations},
	Year = {1977}}

@unpublished{surmey11,
	Author = {A. Surana and S. Meyn},
	Date-Added = {2011-03-04 17:56:48 -0600},
	Date-Modified = {2011-03-04 17:57:05 -0600},
	Note = {Submitted to IEEE Conference on Decision and Control},
	Title = {{TD}-Learning with Exploration},
	Year = {2011}}

@unpublished{yinmehmeysha11,
	Author = {H. Yin and Mehta, P.G. and Meyn, S.P. and Shanbhag, U.V.},
	Date-Added = {2011-03-04 17:40:49 -0600},
	Date-Modified = {2011-03-04 17:40:49 -0600},
	Note = {To appear as a Regular Paper in the {IEEE Transactions on Automatic Control}},
	Title = {Synchronization of coupled oscillators is a game},
	Year = {2010}}

@inproceedings{denmehmey10,
	Author = {K. Deng and Mehta, P.G. and Meyn, S.P.},
	Booktitle = CDC2010,
	Date-Added = {2011-03-04 17:39:01 -0600},
	Date-Modified = {2011-03-04 17:39:01 -0600},
	Pages = {6183-6188},
	Title = {Aggregation-based Model Reduction of a Hidden {Markov} Model},
	Year = {2010}}

@inproceedings{yanmehmey11,
	Author = {T. Yang and P. G. Mehta and S. P. Meyn},
	Booktitle = ACC2011,
	Date-Added = {2011-02-19 14:25:34 -0500},
	Date-Modified = {2011-02-19 14:25:34 -0500},
	Month = {June},
	Title = {A Control-Oriented Approach to Particle Filtering},
	Year = {2011}}

@article{cite-key,
	Date-Added = {2011-02-02 11:43:42 -0600},
	Date-Modified = {2011-02-02 11:43:42 -0600}}

@book{sze10,
	Author = {C. Szepesv{\'a}ri},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2011-01-28 21:21:25 -0600},
	Date-Modified = {2011-01-28 21:21:25 -0600},
	Ee = {http://dx.doi.org/10.2200/S00268ED1V01Y201005AIM009},
	Publisher = {Morgan {\&} Claypool Publishers},
	Series = {Synthesis Lectures on Artificial Intelligence and Machine Learning},
	Title = {Algorithms for Reinforcement Learning},
	Year = {2010}}

@techreport{rumnir94,
	Author = {G. A. Rummery and M. Niranjan},
	Date-Added = {2011-01-28 21:21:25 -0600},
	Date-Modified = {2011-01-28 21:21:25 -0600},
	Institution = {Cambridge Univ., Dept. Eng., Cambridge, U.K. CUED/F-INENG/},
	Number = {166},
	Title = {On-Line {Q}-Learning Using Connectionist Systems},
	Type = {Technical report},
	Year = {1994}}

@article{sinjaalitsze00,
	Abstract = {An important application of reinforcement learning (RL) is to finite-state control problems and one of the most difficult problems in learning for control is balancing the exploration/exploitation tradeoff. Existing theoretical results for RL give very little guidance on reasonable ways to perform exploration. In this paper, we examine the convergence of single-step on-policy RL algorithms for control. On-policy algorithms cannot separate exploration from learning and therefore must confront the exploration problem directly. We prove convergence results for several related on-policy algorithms with both decaying exploration and persistent exploration. We also provide examples of exploration strategies that can be followed during learning that result in convergence to both optimal values and optimal policies.},
	Author = {Singh, S. and Jaakkola, T. and Littman, M. L. and Szepesv\'ari, C.},
	Date-Added = {2011-01-28 21:21:25 -0600},
	Date-Modified = {2011-01-28 21:21:25 -0600},
	Issn = {0885-6125},
	Issue = {3},
	Journal = ML,
	Pages = {287-308},
	Publisher = {Springer Netherlands},
	Title = {Convergence Results for Single-Step On-Policy Reinforcement-Learning Algorithms},
	Url = {http://dx.doi.org/10.1023/A:1007678930559},
	Volume = {38},
	Year = {2000},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1007678930559}}

@unpublished{denmehmey11,
	Author = {K. Deng and Mehta, P.G. and Meyn, S.P.},
	Date-Added = {2011-01-14 10:48:43 -0600},
	Date-Modified = {2011-01-14 10:49:43 -0600},
	Note = {To appear as a Regular Paper in the {IEEE Transactions on Automatic Control}},
	Title = {Optimal {Kullback-Leibler} Aggregation Via the Spectral Theory of {Markov} Chains},
	Year = {2011}}

@inproceedings{yinmehmeysha10,
	Abstract = {The purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents. Applications are found in neuroscience, biology, economics, as well as traditional engineering applications. The focus of analysis is a variation of the large population LQG model of Huang et. al. 2007, comprised here of a controlled nonlinear N-dimensional stochastic differential equation model, coupled only through a nonlinear cost function. The states are interpreted as the phase angle for a collection of non-homogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto. A deterministic PDE model is proposed, which is shown to approximate the stochastic system as the population size approaches infinity. Key to the analysis of the PDE model is the existence of a particular Nash equilibrium in which the agents `opt out' of the game, setting their controls to zero, resulting in the `incoherence' equilibrium. Methods from dynamical systems theory are used in a bifurcation analysis, based on a linearization of the PDE model about the incoherence equilibrium. A critical value of the control cost parameter is identified: Above this value, the oscillators are incoherent; and below this value (when control is sufficiently cheap) the oscillators synchronize. These conclusions are illustrated with results from numerical experiments.},
	Author = {H. Yin and Mehta, P.G. and Meyn, S.P. and Shanbhag, U.V.},
	Booktitle = ACC2010,
	Date-Added = {2011-01-10 19:58:22 -0600},
	Date-Modified = {2011-01-14 10:29:27 -0600},
	Issn = {0743-1619},
	Keywords = {Nash equilibrium;PDE model;bifurcation analysis;coupled heterogeneous nonlinear systems;coupled oscillators synchronization;incoherence equilibrium;large population LQG model;noncooperative dynamic games;nonhomogeneous oscillators;nonlinear N-dimensional stochastic differential equation model;nonlinear cost function;phase transition;stochastic system;bifurcation;game theory;linear quadratic Gaussian control;nonlinear control systems;nonlinear differential equations;oscillators;partial differential equations;stochastic systems;synchronisation;},
	Pages = {1783--1790},
	Title = {Synchronization of coupled oscillators is a game},
	Year = {2010}}

@inproceedings{denmehmey09,
	Abstract = {This paper addresses model reduction for a Markov chain on a large state space. A simulation-based framework is introduced to perform state aggregation of the Markov chain based on observations of a single sample path. The Kullback-Leibler (K-L) divergence rate is employed as a metric to measure the distance between two stationary Markov chains. Model reduction with respect to this metric is cast as an infinite-horizon average cost optimal control problem. In this way an optimal policy corresponds to an optimal partition of the state space with respect to the K-L divergence rate. The optimal control problem is simplified in an approximate dynamic programming (ADP) framework: First, a relaxation of the policy space is performed, and based on this a parameterization of the set of optimal policies is introduced. This makes possible a stochastic approximation approach to compute the best policy within a given parameterized class. The algorithm can be implemented using a single sample path of the Markov chain. Convergence is established using the ODE method. Examples illustrate the theoretical results, and show remarkably low variance and fast convergence.},
	Author = {K. Deng and Mehta, P.G. and Meyn, S.P.},
	Booktitle = CDC2009,
	Date-Added = {2010-12-26 12:08:06 -0600},
	Date-Modified = {2011-01-14 10:46:44 -0600},
	Doi = {10.1109/CDC.2009.5400533},
	Issn = {0191-2216},
	Keywords = {Kullback-Leibler divergence rate;ODE method;aggregating Markov chains;approximate dynamic programming;infinite-horizon average cost optimal control;model reduction;optimal partition;optimal policy;simulation-based framework;simulation-based method;state aggregation;state space;stochastic approximation approach;Markov processes;cost optimal control;dynamic programming;infinite horizon;reduced order systems;state-space methods;},
	Pages = {4710-4716},
	Title = {A simulation-based method for aggregating {Markov} chains},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2009.5400533}}

@inproceedings{densunmehmey09,
	Abstract = {This paper is concerned with an information-theoretic framework to aggregate a large-scale Markov chain to obtain a reduced order Markov model. The Kullback-Leibler (K-L) divergence rate is employed as a metric to measure the distance between two stationary Markov chains. Model reduction is obtained by considering an optimization problem with respect to this metric. The solution is just the optimal aggregated Markov model. We show that the solution of the bi-partition problem is given by an eigenvalue problem. To construct a reduced order model with m super-states, a recursive algorithm is proposed and illustrated with examples.},
	Author = {Deng, K. and Sun, Y. and Mehta, P.G. and Meyn, S.P.},
	Booktitle = ACC2009,
	Date-Added = {2010-12-26 12:07:07 -0600},
	Date-Modified = {2011-01-18 18:21:34 -0600},
	Doi = {10.1109/ACC.2009.5160607},
	Issn = {0743-1619},
	Keywords = {Kullback-Leibler divergence rate;Markov chain;bi-partition problem;eigenvalue problem;information-theoretic framework;model reduction;optimization problem;recursive algorithm;reduced order Markov model;Markov processes;eigenvalues and eigenfunctions;optimisation;reduced order systems;},
	Pages = {731--736},
	Title = {An information-theoretic framework to aggregate a {Markov} chain},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ACC.2009.5160607}}

@article{robtwe00,
	Author = {Roberts, G. O. and Tweedie, R. L.},
	Date-Added = {2010-12-16 09:23:31 -0500},
	Date-Modified = {2010-12-16 09:23:31 -0500},
	Journal = JAP,
	Pages = {359--373},
	Title = {Rates of convergence of stochastically monotone and continuous time {Markov} models},
	Volume = {37},
	Year = {2000}}

@unpublished{wanshazhelitmey10,
	Abstract = {Prices in electricity markets are given by the dual variables
associated with the supply-demand constraint in the dispatch problem.
However, in unit-commitment-based day-ahead markets, these
variables are less easy to obtain. A common approach relies on resolving
the dispatch problem with 
the commitment decisions fixed and utilizing the associated dual
variables. Yet, this avenue leads to inadequate revenues to generators and necessitates an
{\em  uplift payment} to be made by the market operator.
Recently,  a {\em convex hull pricing} scheme has been proposed to
reduce the impact of such payments and requires the global maximization of
the associated Lagrangian dual problem, which is, in general, a
piecewise-affine concave function.  In this paper, we present a
pivot-based finite-termination procedure for obtaining such a global
maximizer. Unlike standard subgradient schemes where an arbitrary
subgradient is used, we present a novel technique
where the {\em steepest} ascent direction is constructed by solving a
continuous quadratic program. The
scheme initiates a move along this direction with an a priori constant
steplength, with the intent of reaching the boundary of the
face. A backtracking scheme allows for mitigating the impact of
excessively large steps. Termination of the scheme occurs when the set
of subgradients contains the zero vector. Preliminary numerical tests
are seen to be promising and display the finite-termination property.
Furthermore, the scheme is seen to significantly outperform standard
subgradient methods.},
	Author = {G. Wang and U. V. Shanbhag and T. Zheng and E. Litvinov and S. P. Meyn},
	Date-Added = {2010-12-01 22:42:08 -0500},
	Date-Modified = {2010-12-01 22:42:55 -0500},
	Keywords = {Convex hull price, electricity markets, uplift payments, nondifferentiable optimization, Lagrangian relaxation.},
	Note = {Proceedings {PESGM} (submitted Nov., 2010)},
	Title = {A Pivot-Based Global Optimization Technique for Convex Hull Pricing},
	Year = {2011}}

@inproceedings{huamey10a,
	Abstract = {This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for this purpose. In prior work it is shown that its finite-observation performance can be much better than the (optimal) Hoeffding test, and good performance depends crucially on the choice of features. The contributions of this paper include: (i) We obtain bounds on the number of #x03B5;-distinguishable distributions in an exponential family. (ii) This motivates a new framework for feature extraction, cast as a rank-constrained optimization problem. (iii) We obtain a gradient-based algorithm to solve the rank-constrained optimization problem and prove its local convergence.},
	Author = {Huang, D. and Meyn, S.P.},
	Booktitle = ISIT2010,
	Date-Added = {2010-11-29 08:35:18 -0600},
	Date-Modified = {2011-01-10 19:59:12 -0600},
	Doi = {10.1109/ISIT.2010.5513384},
	Keywords = {#x03B5;-distinguishable distributions;Hoeffding test;feature extraction;finite observation performance;gradient-based algorithm;local convergence;mismatched universal test;observation space;rank constrained optimization;universal hypothesis testing problems;feature extraction;gradient methods;optimisation;testing;},
	Pages = {1618 -1622},
	Title = {Feature extraction for universal hypothesis testing via rank-constrained optimization},
	Url = {http://arxiv.org/abs/1001.3090v1},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ISIT.2010.5513384}}

@inproceedings{unnmeyvee10a,
	Abstract = {Goodness-of-fit tests are statistical procedures used to test the hypothesis H0 that a set of observations were drawn according to some given probability distribution. Decision thresholds used in goodness-of-fit tests are typically set for guaranteeing a target false-alarm probability. In many popular testing procedures results on the weak convergence of the test statistics are used for setting approximate thresholds when exact computation is infeasible. In this work, we study robust procedures for goodness-of-fit where accurate models are not available for the distribution of the observations under hypothesis H0. We develop procedures for setting thresholds in two specific examples #x2014; a robust version of the Kolmogorov-Smirnov test for continuous alphabets and a robust version of the Hoeffding test for finite alphabets.},
	Author = {Unnikrishnan, J. and Meyn, S. and Veeravalli, V. V.},
	Booktitle = ITW2010,
	Date-Added = {2010-10-22 13:26:08 -0500},
	Date-Modified = {2011-01-10 20:07:51 -0600},
	Doi = {10.1109/CIG.2010.5592803},
	Pages = {1--4},
	Title = {On thresholds for robust goodness-of-fit tests},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CIG.2010.5592803}}

@inproceedings{shimey11,
	Author = {D. Shirodkar and S. P. Meyn},
	Booktitle = ACC2011,
	Date-Added = {2010-10-19 11:51:01 -0500},
	Date-Modified = {2011-01-11 04:54:48 -0600},
	Month = {June},
	Title = {Quasi Stochastic Approximation},
	Year = {2011}}

@article{poljud92,
	Address = {Philadelphia, PA, USA},
	Author = {Polyak, B. T. and Juditsky, A. B.},
	Date-Added = {2010-09-21 20:37:45 -0500},
	Date-Modified = {2010-09-21 20:37:45 -0500},
	Doi = {http://dx.doi.org/10.1137/0330046},
	Issn = {0363-0129},
	Journal = SICON,
	Number = {4},
	Pages = {838--855},
	Publisher = {Society for Industrial and Applied Mathematics},
	Title = {Acceleration of stochastic approximation by averaging},
	Volume = {30},
	Year = {1992},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/0330046}}

@article{katvei87,
	Abstract = {The multi-armed bandit problem arises in sequentially allocating effort to one of N projects and sequentially assigning patients to one of N treatments in clinical trials. Gittins and Jones (1974) have shown that one optimal policy for the N-project problem, an N-dimensional discounted Markov decision chain, is determined by the following largest-index rule. There is an index for each state of each given project that depends only on the data of that project. In each period one allocates effort to a project with largest current index. The purpose of this paper is to give a short proof of this result and a new characterization of the index of a project in state i, viz., as the maximum expected present value in state i for the restart-in-i problem in which, in each state and period, one either continues allocating effort to the project or immediately restarts the project in state i. Moreover, it is shown that an approximate largest-index rule yields an approximately optimal policy. These results lead to more efficient methods of computing the indices on-line and/or for sparse transition matrices in large state spaces than have been suggested heretofore. By using a suitable implementation of successive approximations, a policy whose expected present value is within $\epsilon$ \% of the maximum possible range of values of the indices can be found on-line with at most (N + T - 1)TM operations where M is the number of operations required to calculate one approximation, T is the least integer majorizing the ratio ln $\epsilon$ /ln a and 0 < a < 1 is the discount factor.},
	Author = {Katehakis, M. N. and Veinott, A. F., Jr.},
	Date-Added = {2010-09-03 12:49:21 -0500},
	Date-Modified = {2010-09-03 12:49:55 -0500},
	Issn = {0364765X},
	Journal = MOR,
	Language = {English},
	Number = {2},
	Pages = {262-268},
	Publisher = {INFORMS},
	Title = {The Multi-Armed Bandit Problem: Decomposition and Computation},
	Url = {http://www.jstor.org/stable/3689689},
	Volume = {12},
	Year = {1987},
	Bdsk-Url-1 = {http://www.jstor.org/stable/3689689}}

@article{lez98,
	Author = {Lezaud, Pascal},
	Date-Added = {2010-08-06 11:19:25 -0500},
	Date-Modified = {2010-08-06 11:19:38 -0500},
	Doi = {10.1214/aoap/1028903453},
	Fjournal = {The Annals of Applied Probability},
	Issn = {1050-5164},
	Journal = {Ann. Appl. Probab.},
	Mrclass = {60F10 (60J10)},
	Mrnumber = {MR1627795 (99f:60061)},
	Mrreviewer = {Ofer Zeitouni},
	Number = {3},
	Pages = {849--867},
	Title = {Chernoff-type bound for finite {M}arkov chains},
	Url = {http://dx.doi.org/10.1214/aoap/1028903453},
	Volume = {8},
	Year = {1998},
	Bdsk-Url-1 = {http://dx.doi.org/10.1214/aoap/1028903453}}

@article{sharajsma08,
	Author = {M. Shashanka and B. Raj and P. Smaragdis},
	Date-Added = {2010-07-28 15:28:09 -0700},
	Date-Modified = {2010-07-28 15:29:36 -0700},
	Journal = {Computational Intelligence and Neuroscience},
	Pages = {1-8},
	Title = {{Probabilistic Latent Variable Models} as Nonnegative Factorizations},
	Year = {2008}}

@inproceedings{gaugou05,
	Address = {New York, NY, USA},
	Author = {Gaussier, Eric and Goutte, Cyril},
	Booktitle = {SIGIR '05: Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval},
	Date-Added = {2010-07-28 15:22:31 -0700},
	Date-Modified = {2010-07-28 15:23:14 -0700},
	Doi = {http://doi.acm.org/10.1145/1076034.1076148},
	Isbn = {1-59593-034-5},
	Location = {Salvador, Brazil},
	Pages = {601--602},
	Publisher = {ACM},
	Title = {Relation between {PLSA and NMF} and implications},
	Year = {2005},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/1076034.1076148}}

@article{hof01,
	Address = {Hingham, MA, USA},
	Author = {Hofmann, Thomas},
	Date-Added = {2010-07-28 15:20:58 -0700},
	Date-Modified = {2010-07-28 15:20:58 -0700},
	Doi = {http://dx.doi.org/10.1023/A:1007617005950},
	Issn = {0885-6125},
	Journal = {Mach. Learn.},
	Number = {1-2},
	Pages = {177--196},
	Publisher = {Kluwer Academic Publishers},
	Title = {Unsupervised Learning by {Probabilistic Latent Semantic Analysis}},
	Volume = {42},
	Year = {2001},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1007617005950}}

@article{bercas91,
	Author = {D. P. Bertsekas and D. A. Casta{\~n}on},
	Date-Added = {2010-07-21 08:48:43 -0400},
	Date-Modified = {2010-07-21 08:49:51 -0400},
	Journal = {Parallel Computing},
	Number = {6-7},
	Pages = {707-732},
	Title = {Parallel synchronous and asynchronous implementations of the auction algorithm},
	Volume = {17},
	Year = {1991}}

@article{craishlio92,
	Author = {Crandall, M. G. and Ishii, H. and Lions, P.-L.},
	Date-Added = {2010-05-29 17:31:36 -0500},
	Date-Modified = {2010-05-29 17:31:36 -0500},
	Fjournal = {American Mathematical Society. Bulletin. New Series},
	Journal = {Bull. Amer. Math. Soc. (N.S.)},
	Number = {1},
	Pages = {1--67},
	Title = {User's guide to viscosity solutions of second order partial differential equations},
	Volume = {27},
	Year = {1992}}

@book{fleson93a,
	Address = {New York},
	Author = {Fleming, W. H. and Soner, H. M.},
	Date-Added = {2010-05-29 17:30:56 -0500},
	Date-Modified = {2010-05-29 17:30:56 -0500},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Controlled {M}arkov processes and viscosity solutions},
	Volume = {25},
	Year = {1993}}

@article{ros68a,
	Author = {Ross, S. M.},
	Date-Added = {2010-05-29 17:27:25 -0500},
	Date-Modified = {2010-08-23 18:42:20 -0500},
	Journal = ANNMS,
	Number = {1},
	Pages = {2118--2122},
	Title = {Arbitrary State {Markovian} Decision Processes},
	Volume = {39},
	Year = {1968}}

@article{anavarwal87b,
	Author = {Anantharam, Venkatachalam and Varaiya, Pravin and Walrand, Jean},
	Coden = {IETAA9},
	Date-Added = {2010-05-20 08:27:35 -0500},
	Date-Modified = {2010-05-20 08:27:35 -0500},
	Doi = {10.1109/TAC.1987.1104485},
	Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control},
	Issn = {0018-9286},
	Journal = {IEEE Trans. Automat. Control},
	Mrclass = {62L15 (90C40)},
	Mrnumber = {MR909967 (89h:62141)},
	Mrreviewer = {Masami Kurano},
	Number = {11},
	Pages = {977--982},
	Title = {Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays. {II}. {M}arkovian rewards},
	Url = {http://dx.doi.org/10.1109/TAC.1987.1104485},
	Volume = {32},
	Year = {1987},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TAC.1987.1104485}}

@article{anavarwal87a,
	Author = {Anantharam, Venkatachalam and Varaiya, Pravin and Walrand, Jean},
	Coden = {IETAA9},
	Date-Added = {2010-05-20 08:27:35 -0500},
	Date-Modified = {2010-05-20 08:27:35 -0500},
	Doi = {10.1109/TAC.1987.1104491},
	Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control},
	Issn = {0018-9286},
	Journal = {IEEE Trans. Automat. Control},
	Mrclass = {62L15 (90C40)},
	Mrnumber = {MR909966 (89h:62140)},
	Mrreviewer = {Masami Kurano},
	Number = {11},
	Pages = {968--976},
	Title = {Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays. {I}.\ {I}.{I}.{D}.\ rewards},
	Url = {http://dx.doi.org/10.1109/TAC.1987.1104491},
	Volume = {32},
	Year = {1987},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TAC.1987.1104491}}

@article{lairob85,
	Author = {Lai, T. L. and Robbins, Herbert},
	Date-Added = {2010-05-20 08:27:35 -0500},
	Date-Modified = {2010-05-20 08:27:35 -0500},
	Doi = {10.1016/0196-8858(85)90002-8},
	Fjournal = {Advances in Applied Mathematics},
	Issn = {0196-8858},
	Journal = {Adv. in Appl. Math.},
	Mrclass = {62L05},
	Mrnumber = {MR776826 (86i:62169)},
	Mrreviewer = {Albrecht Irle},
	Number = {1},
	Pages = {4--22},
	Title = {Asymptotically efficient adaptive allocation rules},
	Url = {http://dx.doi.org/10.1016/0196-8858(85)90002-8},
	Volume = {6},
	Year = {1985},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0196-8858(85)90002-8}}

@article{zhofumar10,
	Abstract = { Research on numerical solution methods for partially observable Markov decision processes (POMDPs) has primarily focused on finite-state models, and these algorithms do not generally extend to continuous-state POMDPs, due to the infinite dimensionality of the belief space. In this paper, we develop a computationally viable and theoretically sound method for solving continuous-state POMDPs by effectively reducing the dimensionality of the belief space via density projection. The density projection technique is also incorporated into particle filtering to provide a filtering scheme for online decision making. We provide an error bound between the value function induced by the policy obtained by our method and the true value function of the POMDP, and also an error bound between projection particle filtering and exact filtering. Finally, we illustrate the effectiveness of our method through an inventory control problem. },
	Author = {Zhou, E. and Fu, M. C. and Marcus, S. I.},
	Date-Added = {2010-05-10 20:57:04 -0500},
	Date-Modified = {2010-05-10 20:58:00 -0500},
	Doi = {10.1109/TAC.2010.2042005},
	Issn = {0018-9286},
	Journal = TAC,
	Number = {5},
	Pages = {1101 -1116},
	Title = {Solving Continuous-State {POMDP}s via Density Projection},
	Volume = {55},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TAC.2010.2042005}}

@article{fel59,
	Author = {Feller, William},
	Date-Added = {2010-05-04 07:05:53 -0700},
	Date-Modified = {2010-05-04 07:05:53 -0700},
	Issn = {00034851},
	Journal = {The Annals of Mathematical Statistics},
	Jstor_Formatteddate = {Dec., 1959},
	Number = {4},
	Pages = {1252--1253},
	Publisher = {Institute of Mathematical Statistics},
	Title = {{Non-Markovian} Processes with the Semigroup Property},
	Url = {http://www.jstor.org/stable/2237470},
	Volume = {30},
	Year = {1959},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2237470}}

@book{chuwil90,
	Author = {Chung, K. L. and Williams, R. J.},
	Date-Added = {2010-03-18 22:20:13 -0400},
	Date-Modified = {2010-03-27 16:21:08 -0500},
	Publisher = {{Birkh\"{a}user Boston}},
	Series = {Prob. and its Appls.},
	Title = {An Introduction to Stochastic Integration},
	Year = {1990}}

@article{dhuorl06,
	Abstract = {Recent work has considered encoding a string by separately conveying its symbols and its pattern-the order in which the symbols appear. It was shown that the patterns of independent and identically distributed (i.i.d.) strings can be losslessly compressed with diminishing per-symbol redundancy. In this correspondence, the pattern redundancy of distributions with memory is considered. Close lower and upper bounds are established on the pattern redundancy of strings generated by Hidden {Markov} models (HMMs) with a small number of states, showing in particular that their per-symbol pattern redundancy diminishes with increasing string length. The upper bounds are obtained by analyzing the growth rate of the number of multidimensional integer partitions, and the lower bounds, using Hayman's theorem},
	Author = {Dhulipala, A.K. and Orlitsky, A.},
	Date-Added = {2010-02-17 10:41:23 -0600},
	Date-Modified = {2010-09-15 21:47:28 -0500},
	Doi = {10.1109/TIT.2006.880013},
	Issn = {0018-9448},
	Journal = TIT,
	Keywords = {HMM;arbitrary alphabet;hidden {Markov} model;pattern redundancy;string encoding;universal compression;data compression;hidden {Markov} models;source coding;},
	Month = {Sept.},
	Number = {9},
	Pages = {4182 -4190},
	Title = {Universal Compression of {Markov} and Related Sources Over Arbitrary Alphabets},
	Volume = {52},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TIT.2006.880013}}

@inproceedings{dhufraorl06,
	Abstract = {We consider a power-efficient communication model for wireless sensor networks where silence is used to convey information. We study the average-case and worst-case complexities of symmetric functions under this model and describe protocols that achieve them. For binary-input functions, we determine the average complexity. For ternary-input functions, we consider a special type of protocols and provide close lower and upper bounds for their worst-case complexity. We also describe the protocol that achieves the average complexity},
	Author = {Dhulipala, A.K. and Fragouli, C. and Orlitsky, A.},
	Booktitle = {Proc. of the {IEEE International Symposium on Information Theory}},
	Date-Added = {2010-02-17 10:41:23 -0600},
	Date-Modified = {2010-09-15 21:43:14 -0500},
	Doi = {10.1109/ISIT.2006.261835},
	Keywords = {average-case complexity;binary-input functions;power-efficient communication model;silence based communication;symmetric functions;ternary-input functions;wireless sensor networks;worst-case complexity;protocols;wireless sensor networks;},
	Month = {July},
	Pages = {212 -216},
	Title = {Silence Based Communication for Sensor Networks},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ISIT.2006.261835}}

@inproceedings{huaunnmeyveesur09,
	Abstract = {The support vector machine (SVM) has emerged as one of the most popular approaches to classification and supervised learning. It is a flexible approach for solving the problems posed in these areas, but the approach is not easily adapted to noisy data in which absolute discrimination is not possible. We address this issue in this paper by returning to the statistical setting. The main contribution is the introduction of a statistical support vector machine (SSVM) that captures all of the desirable features of the SVM, along with desirable statistical features of the classical likelihood ratio test. In particular, we establish the following: (i) The SSVM can be designed so that it forms a continuous function of the data, yet also approximates the potentially discontinuous log likelihood ratio test. (ii) Extension to universal detection is developed, in which only one hypothesis is labeled (a semi-supervised learning problem). (iii) The SSVM generalizes the robust hypothesis testing problem based on a moment class. Motivation for the approach and analysis are each based on ideas from information theory. A detailed performance analysis is provided in the special case of i.i.d. observations. This research was partially supported by NSF under grant CCF 07-29031, by UTRC, Motorola, and by the DARPA ITMANET program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF, UTRC, Motorola, or DARPA.},
	Author = {Dayu Huang and Unnikrishnan, J. and Meyn, S. P. and Veeravalli, V. and Surana, A.},
	Booktitle = ITW2009,
	Date-Added = {2010-02-03 17:20:55 -0600},
	Date-Modified = {2011-01-10 20:03:26 -0600},
	Doi = {10.1109/ITWNIT.2009.5158542},
	Keywords = {learning (artificial intelligence), support vector machinesrobust detection, statistical SVM, supervised learning, support vector machine, universal classification},
	Pages = {62--66},
	Title = {Statistical {SVMs} for robust detection, supervised learning, and universal classification},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ITWNIT.2009.5158542}}

@inproceedings{unnveemey09,
	Abstract = {We study the problem of robust quickest change detection where the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions. Both Bayesian and minimax versions of the quickest change detection problem are considered. When the uncertainty classes satisfy some specific conditions, we identify least favorable distributions (LFD's) from the uncertainty classes, and show that the detection rule designed for the LFD's is optimal in a minimax sense. The condition is similar to that required for the existence of LFD's for the robust hypothesis testing problem studied by Huber.},
	Author = {Unnikrishnan, J. and Veeravalli, V.V. and Meyn, S.},
	Booktitle = ISIT2009,
	Date-Added = {2010-02-03 17:19:01 -0600},
	Date-Modified = {2011-01-10 20:02:16 -0600},
	Doi = {10.1109/ISIT.2009.5205661},
	Keywords = {minimax techniques, statistical distributionschange detection problem, detection rule, least favorable distribution, minimax version, postchange distribution, prechange distribution, robust quickest change detection, uncertainty classes},
	Pages = {649-653},
	Title = {Least favorable distributions for robust quickest change detection},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ISIT.2009.5205661}}

@inproceedings{mehmey09a,
	Abstract = {Q-learning is a technique used to compute an optimal policy for a controlled Markov chain based on observations of the system controlled using a non-optimal policy. It has proven to be effective for models with finite state and action space. This paper establishes connections between Q-learning and nonlinear control of continuous-time models with general state space and general action space. The main contributions are summarized as follows. (i) The starting point is the observation that the "Q-function" appearing in Q-learning algorithms is an extension of the Hamiltonian that appears in the minimum principle. Based on this observation we introduce the steepest descent Q-learning algorithm to obtain the optimal approximation of the Hamiltonian within a prescribed function class, (ii) A transformation of the optimality equations is performed based on the adjoint of a resolvent operator. This is used to construct a consistent algorithm based on stochastic approximation that requires only causal filtering of observations, (iii) Several examples are presented to illustrate the application of these techniques, including application to distributed control of multi-agent systems},
	Author = {Mehta, P. G. and Meyn, S. P.},
	Booktitle = CDC2009,
	Date-Added = {2010-02-03 17:05:25 -0600},
	Date-Modified = {2011-01-28 15:14:28 -0600},
	Doi = {10.1109/CDC.2009.5399753},
	Issn = {0191-2216},
	Month = {Dec.},
	Pages = {3598-3605},
	Title = {Q-learning and {Pontryagin's} Minimum Principle},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2009.5399753}}

@inproceedings{meysurlinnar09,
	Abstract = {The paper develops application of techniques from robust and universal hypothesis testing for anomaly detection and change-point detection in dynamic, interconnected systems. This theory is extended using the concept of projected {Markov} models originally proposed by Claude Shannon. Also presented is a detailed application to anomaly detection from people movements patterns in buildings.},
	Author = {Meyn, S. P. and Surana, A. and Lin, Y. and Narayanan, S.},
	Booktitle = CDC2009,
	Date-Added = {2010-02-03 17:04:21 -0600},
	Date-Modified = {2011-01-14 09:38:40 -0600},
	Doi = {10.1109/CDC.2009.5400612},
	Issn = {0191-2216},
	Keywords = {anomaly detection;change-point detection;distributed sensor network;hypothesis testing;interconnected systems;projective Markov models;Markov processes;distributed sensors;large-scale systems;pattern recognition},
	Pages = {4662--4669},
	Title = {Anomaly detection using projective {Markov} models in a distributed sensor network},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2009.5400612}}

@article{budchelee07,
	Abstract = {
The main goal of filtering is to obtain, recursively in time, good estimates of the state of a stochastic dynamical system based on noisy partial observations of the same. In settings where the signal/observation dynamics are significantly nonlinear or the noise intensities are high, an extended Kalman filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, can perform quite poorly: it may require very frequent re-initializations and in some situations may even diverge. The theory of nonlinear filtering addresses these difficulties by considering the evolution of the conditional distribution of the state of the system given all the available observations, in the space of probability measures. We survey a variety of numerical schemes that have been developed in the literature for approximating the conditional distribution described by such stochastic evolution equations; with a special emphasis on an important family of schemes known as the particle filters. A numerical study is presented to illustrate that in settings where the signal/observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended Kalman filter.},
	Author = {Amarjit Budhiraja and Lingji Chen and Chihoon Lee},
	Date-Added = {2010-01-25 20:26:53 -0600},
	Date-Modified = {2010-01-25 20:27:51 -0600},
	Doi = {DOI: 10.1016/j.physd.2006.08.015},
	Issn = {0167-2789},
	Journal = {Physica D: Nonlinear Phenomena},
	Keywords = {Nonlinear filtering,Extended Kalman filter,Particle filters,Sequential importance sampling,Kallianpur-Striebel formula},
	Number = {1-2},
	Pages = {27 - 36},
	Title = {A survey of numerical methods for nonlinear filtering problems},
	Url = {http://www.sciencedirect.com/science/article/B6TVK-4M2WNVT-2/2/1e50b641f6d484aacab2c9aa19a0db3b},
	Volume = {230},
	Year = {2007},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6TVK-4M2WNVT-2/2/1e50b641f6d484aacab2c9aa19a0db3b},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2006.08.015}}

@inproceedings{bormey08a,
	Address = {ICST, Brussels, Belgium, Belgium},
	Author = {Borkar, V. and Meyn, S. P.},
	Booktitle = {{ValueTools '08: Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools}},
	Date-Added = {2009-12-31 13:47:40 -0600},
	Date-Modified = {2009-12-31 13:47:40 -0600},
	Doi = {http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4600},
	Isbn = {978-963-9799-31-8},
	Location = {Athens, Greece},
	Pages = {1--7},
	Publisher = {ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)},
	Title = {Oja's algorithm for graph clustering and {Markov} spectral decomposition},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4600}}

@inproceedings{kyrkonmey08,
	Address = {ICST, Brussels, Belgium, Belgium},
	Author = {Kyriazopoulou-Panagiotopoulou, S. and Kontoyiannis, I. and Meyn, S. P.},
	Booktitle = {ValueTools '08: Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools},
	Date-Added = {2009-12-31 13:45:21 -0600},
	Date-Modified = {2009-12-31 13:45:21 -0600},
	Doi = {http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4242},
	Isbn = {978-963-9799-31-8},
	Location = {Athens, Greece},
	Pages = {1--9},
	Publisher = {ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)},
	Title = {Control variates as screening functions},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.4242}}

@inproceedings{melmeyrib08,
	Address = {New York, NY, USA},
	Author = {Melo, F. S. and Meyn, S. P. and Ribeiro, M. I.},
	Booktitle = {{ICML '08: Proceedings of the 25th international conference on Machine learning}},
	Date-Added = {2009-12-31 13:39:24 -0600},
	Date-Modified = {2009-12-31 13:39:24 -0600},
	Doi = {http://doi.acm.org/10.1145/1390156.1390240},
	Isbn = {978-1-60558-205-4},
	Location = {Helsinki, Finland},
	Pages = {664--671},
	Publisher = {ACM},
	Title = {An analysis of reinforcement learning with function approximation},
	Year = {2008},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/1390156.1390240}}

@article{tsiroy99,
	Author = {Tsitsiklis, J. N. and Van Roy, B.},
	Coden = {IETAA9},
	Date-Added = {2009-12-16 20:41:23 +0800},
	Date-Modified = {2009-12-16 20:41:23 +0800},
	Doi = {10.1109/9.793723},
	Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Automatic Control},
	Issn = {0018-9286},
	Journal = TAC,
	Mrclass = {60G40 (60J05 90C40 91B28)},
	Mrnumber = {MR1716061 (2000g:60074)},
	Number = {10},
	Pages = {1840--1851},
	Title = {Optimal stopping of {M}arkov processes: {H}ilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives},
	Url = {http://dx.doi.org/10.1109/9.793723},
	Volume = {44},
	Year = {1999},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/9.793723}}

@inproceedings{yukbasmey08b,
	Abstract = {For Markov sources, the structure of optimal causal encoders minimizing the total communication rate subject to a mean-square distortion constraint is studied. The class of sources considered lives in a continuous alphabet, and the encoder is allowed to be variable-rate. Both the finite-horizon and the infinite-horizon problems are considered. In the finite-horizon case, the problem is non-convex, whereas in the infinite-horizon case the problem can be convexified under certain assumptions. For a finite horizon problem, the optimal deterministic causal encoder for a kth-order Markov source uses only the most recent k source symbols and the information available at the receiver, whereas the optimal causal coder for a memoryless source is memoryless. For the infinite-horizon problem, a convex-analytic approach is adopted. Randomized stationary quantizers are suboptimal in the absence of common randomness between the encoder and the decoder. If there is common randomness, the optimal quantizer requires the randomization of at most two deterministic quantizers. In the absence of common randomness, the optimal quantizer is non-stationary and a recurrence-based time-sharing of two deterministic quantizers is optimal. A linear source driven by Gaussian noise is considered. If the process is stable, innovation coding is almost optimal at high-rates, whereas if the source is unstable, then even a high-rate time-invariant innovation coding scheme leads to an unstable estimation process},
	Author = {Yuksel, S. and Basar, T. and Meyn, S.P.},
	Booktitle = {Information Theory and Applications Workshop, 2008},
	Date-Added = {2009-12-06 11:46:52 -0600},
	Date-Modified = {2010-11-29 09:08:18 -0600},
	Doi = {10.1109/ITA.2008.4601015},
	Keywords = {Gaussian noise, {Markov} processes, distortion, quantisation (signal) Gaussian noise, {Markov} sources, convex-analytic approach, infinite-horizon problem, mean-square distortion constraint, optimal causal quantization, optimal deterministic causal encoder, randomized stationary quantizers, time-invariant innovation coding},
	Month = {27 2008-Feb. 1},
	Pages = {26-30},
	Title = {Optimal causal quantization of {Markov} Sources with distortion constraints},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ITA.2008.4601015}}

@article{pezheu97,
	Author = {Pezeshki-Esfahani, H. and Heunis, A.J.},
	Date-Added = {2009-12-04 18:47:06 -0600},
	Date-Modified = {2009-12-04 18:47:06 -0600},
	Doi = {10.1109/18.556109},
	Issn = {0018-9448},
	Journal = TIT,
	Keywords = {Markov processes, approximation theory, data communication, delta modulation, digital communication, recursive estimationadaptive predictive delta modulation, conditionally Markovian data, data communication, digital communication, discontinous right-hand sides, estimation algorithm, recursive stochastic algorithms, stochastic approximation algorithm, strong diffusion approximations},
	Month = {Mar},
	Number = {2},
	Pages = {512-523},
	Title = {Strong diffusion approximations for recursive stochastic algorithms},
	Volume = {43},
	Year = {1997},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/18.556109}}

@misc{huaunnmeyveesur09a,
	Author = {Unnikrishnan, J. and Huang, D. and Meyn, S. P. and Surana, A. and Veeravalli, V.},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-11-19 13:36:20 -0600},
	Date-Modified = {2010-08-26 17:06:07 -0500},
	Ee = {http://arxiv.org/abs/0909.2234},
	Howpublished = {CoRR and to appear, {IEEE Trans. IT}.},
	Keywords = {Hypothesis testing; Information theory; Support Vector Machine},
	Title = {Universal and Composite Hypothesis Testing via Mismatched Divergence},
	Volume = {abs/0909.2234},
	Year = {2009}}

@misc{unnveemey09b,
	Author = {J. Unnikrishnan and Venugopal V. Veeravalli and Sean Meyn},
	Date-Added = {2009-11-18 14:55:18 -0600},
	Date-Modified = {2011-01-27 08:13:46 -0600},
	Howpublished = {To appear, {IEEE Trans. IT}.},
	Title = {Minimax Robust Quickest Change Detection},
	Url = {http://www.citebase.org/abstract?id=oai:arXiv.org:0911.2551},
	Year = {2009},
	Bdsk-Url-1 = {http://www.citebase.org/abstract?id=oai:arXiv.org:0911.2551}}

@inproceedings{matmey08,
	Abstract = {The goal of this paper is to develop modeling techniques for complex systems for the purposes of control, estimation, and inference: (i) A new class of hidden {Markov} models is introduced, called the optimal feature prediction (OFP) model. It is similar to the Gaussian mixture model in which the actual marginal distribution is used in place of a Gaussian distribution. This structure leads to simple learning algorithms to find an optimal model. (ii) The OFP model provides a unification of other modeling approaches including the projective methods of Shannon, Mori and Zwanzig, and Chorin, as well as a version of the binning technique for {Markov} model reduction. (iii) Several general applications are surveyed, including inference and optimal control. Computation of the spectrum, or solutions to dynamic programming equations are possible through a finite dimensional matrix calculation without knowledge of the underlying marginal distribution on which the model is based.},
	Author = {Meyn, S. P. and Mathew, G.},
	Booktitle = {Proc. 47th IEEE CDC},
	Date-Added = {2009-09-03 21:52:08 -0500},
	Date-Modified = {2009-09-03 21:53:06 -0500},
	Issn = {0191-2216},
	Pages = {5558-5564},
	Title = {Shannon meets {Bellman}: Feature based {Markovian} models for detection and optimization},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2008.4739405}}

@inproceedings{yuber07,
	Author = {H. Yu and D. P. Bertsekas},
	Booktitle = {Proc. European Control Conference (ECC)},
	Date-Added = {2009-08-31 13:56:29 -0500},
	Date-Modified = {2009-08-31 13:56:29 -0500},
	Month = {July},
	Title = {Q-Learning Algorithms for Optimal Stopping Based on Least Squares},
	Year = {2007}}

@misc{farsauwei08,
	Author = {V. F. Farias and D. Saure and G. Y. Weintraub},
	Date-Added = {2009-08-31 13:28:03 -0500},
	Date-Modified = {2009-08-31 13:29:16 -0500},
	Howpublished = {{http://www.stanford.edu/~bvr/publ-all.html}},
	Title = {The linear programming approach to solving large scale dynamic stochastic games (working paper)},
	Year = {2008}}

@incollection{cogrotvanlal06,
	Abstract = {We consider the problem of computing decentralized control policies for stochastic systems with finite state and action spaces. Synthesis of optimal decentralized policies for such problems is known to be NP-hard [1]. Here we focus on methods for efficiently computing meaningful suboptimal decentralized control policies. The algorithms we present here are based on approximation of optimal Q-functions. We show that the performance loss associated with choosing decentralized policies with respect to an approximate Q-function is related to the approximation error.},
	Author = {Cogill, R. and Rotkowitz, M. and Van Roy, B. and Lall, S},
	Booktitle = {Control of Uncertain Systems: Modelling, Approximation, and Design},
	Date-Added = {2009-08-31 13:26:50 -0500},
	Date-Modified = {2009-08-31 13:28:44 -0500},
	Doi = {10.1007/11664550\_13},
	Pages = {243--256},
	Publisher = {Springer},
	Title = {An Approximate Dynamic Programming Approach to Decentralized Control of Stochastic Systems},
	Url = {http://dx.doi.org/10.1007/11664550\_13},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/11664550%5C_13}}

@book{frewen98,
	Address = {New York},
	Author = {Freidlin, M. I. and Wentzell, A. D.},
	Date-Added = {2009-08-29 14:52:53 -0500},
	Date-Modified = {2009-08-29 14:52:53 -0500},
	Edition = {Second},
	Isbn = {0-387-98362-7},
	Mrclass = {60H25 (34C29 34C35 34F05 58F30 60F10)},
	Mrnumber = {MR1652127 (99h:60128)},
	Note = {Translated from the 1979 Russian original by Joseph Sz{\"u}cs},
	Pages = {xii+430},
	Publisher = {Springer-Verlag},
	Series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]},
	Title = {Random perturbations of dynamical systems},
	Volume = {260},
	Year = {1998}}

@article{wen72,
	Abstract = {Let $D$ be a bounded subset of $E^r$ with a smooth boundary $\partial D$, and let $L^\varepsilon=(\varepsilon^2/2)\sum_{i,j}a^{ij}\,\partial^2/\partial x^i\partial x^j+\sum b^i\,\partial/\partial x^i$ be an elliptic operator on $D$, $\varepsilon$ is a small parameter. For $\varphi_t=(\varphi_t{}^1,\varphi_t{}^2,\cdots,\varphi_t{}^r)$, $T_1\leq t\leq T_2$, an absolutely continuous function, define the functional $I(\varphi)=I_{T_1,T_2}(\varphi)$ by $I(\varphi)=\int_{T_1}^{T_2}\sum_{i,j}a_{ij}(\varphi_t)[\dot\varphi_t{}^i-b^i(\varphi_t)][\dot\varphi_j-b_j(\varphi_t)]\,dt$, where the matrix $(a_{ij}(x))$ is the inverse of $(a^{ij}(x))$. Define also $V(x,y)=\inf\{I(\varphi)|\varphi_{T_1}=x,\varphi_{T_2}=y\}$ and let $\lambda_1{}^\varepsilon$ be the largest eigen-value of the operator $L^\varepsilon$ on $D$ with zero boundary values on $\partial D$. The following theorem is proved: Suppose the domain $D$ is such that all the solutions of the system of ordinary differential equations $\dot x_t=b(x_t)$, $b=(b^1,b^2,\cdots,b^r)$, starting from a point in $D\cup\partial D$ and not leaving this set, converge to a point of stable equilibrium $x_0\in D$. Then $\lim_{\varepsilon\rightarrow 0}2\varepsilon^2\ln|\lambda_1{}^\varepsilon|=-\min_{y\in\partial D}V(x_0,y)$.

},
	Author = {Wentzell, A. D.},
	Date-Added = {2009-08-29 14:52:53 -0500},
	Date-Modified = {2009-08-29 14:53:12 -0500},
	Fjournal = {Doklady Akademii Nauk SSSR},
	Issn = {0002-3264},
	Journal = {Dokl. Akad. Nauk SSSR},
	Mrclass = {35B25 (60J45)},
	Mrnumber = {MR0308573 (46 \#7687)},
	Mrreviewer = {D. A. Darling},
	Pages = {19--22},
	Title = {The asymptotic behavior of the largest eigenvalue of a second order elliptic differential operator with a small parameter multiplying the highest derivatives},
	Volume = {202},
	Year = {1972}}

@book{MT,
	Address = {Cambridge},
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Added = {2009-08-18 13:26:01 -0500},
	Date-Modified = {2011-03-18 14:45:55 -0500},
	Edition = {Second},
	Isbn = {978-0-521-73182-9},
	Mrclass = {60J05},
	Mrnumber = {MR2509253},
	Note = {Published in the Cambridge Mathematical Library. 1993 edition online.},
	Pages = {xxviii+594},
	Publisher = {Cambridge University Press},
	Title = {Markov chains and stochastic stability},
	Year = {2009}}

@article{zeizivmer92,
	Author = {O. Zeitouni and J. Ziv and N. Merhav},
	Date-Added = {2009-08-11 16:22:00 -0500},
	Date-Modified = {2009-08-11 16:22:42 -0500},
	Journal = TIT,
	Number = {5},
	Pages = {1597-1602},
	Title = {When is the generalized likelihood ratio test optimal?},
	Volume = {38},
	Year = {1992}}

@article{levmer02,
	Author = {E. Levitan and N. Merhav},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-08-11 12:46:41 -0500},
	Date-Modified = {2009-08-11 12:47:34 -0500},
	Journal = TIT,
	Number = {8},
	Pages = {2215-2229},
	Title = {A competitive {Neyman-Pearson} approach to universal hypothesis testing with applications},
	Volume = {48},
	Year = {2002}}

@article{kontsi04,
	Abstract = {We study the rate of convergence of linear two-time-scale stochastic approximation methods. We consider two-time-scale linear iterations driven by i.i.d. noise, prove some results on their asymptotic covariance and establish asymptotic normality. The well-known result [Polyak, B. T. (1990). Automat. Remote Contr. 51 937-946; Ruppert, D. (1988). Technical Report 781, Cornell Univ.] on the optimality of Polyak-Ruppert averaging techniques specialized to linear stochastic approximation is established as a consequence of the general results in this paper.},
	Author = {Konda, V. R. and Tsitsiklis, J. N.},
	Date-Added = {2009-08-06 09:18:21 -0500},
	Date-Modified = {2009-08-06 09:18:21 -0500},
	Issn = {10505164},
	Journal = ANNAP,
	Number = {2},
	Pages = {796--819},
	Title = {Convergence Rate of Linear Two-Time-Scale Stochastic Approximation},
	Url = {http://www.jstor.org/stable/4140429},
	Volume = {14},
	Year = {2004},
	Bdsk-Url-1 = {http://www.jstor.org/stable/4140429}}

@techreport{ravwailaf09,
	Abstract = {We consider the problem of estimating the graph associated with a binary Ising {Markov} random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional
scaling, in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n =(d3 log p), with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n =
(d2 log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete {Markov} random fields.
},
	Author = {P. Ravikumar and M. J. Wainwright and J. Lafferty},
	Date-Added = {2009-07-20 17:00:08 -0500},
	Date-Modified = {2009-07-20 17:02:55 -0500},
	Institution = {{UC Berkeley}},
	Note = {To appear in the {Annals of Statistics}},
	Title = {High-dimensional Ising model selection using {$\ell_1$}-regularized logistic regression},
	Url = {www.stat.berkeley.edu/~pradeepr/paperz/IsingModelSelectionAOS.pdf},
	Year = {2009},
	Bdsk-Url-1 = {www.stat.berkeley.edu/~pradeepr/paperz/IsingModelSelectionAOS.pdf}}

@article{mer91,
	Author = {Merhav, N.},
	Date-Added = {2009-07-20 16:55:57 -0500},
	Date-Modified = {2009-07-20 16:55:57 -0500},
	Doi = {10.1109/18.104319},
	Issn = {0018-9448},
	Journal = TIT,
	Keywords = {Markov processes, data compression, information theory, speech recognitionHMM, Neyman-Pearson formulation, asymptotically optimal decision rule, binary hypothesis testing, communication applications, generalized likelihood ratio test, hidden {Markov} model, speech recognition, universal classification},
	Month = {Nov},
	Number = {6},
	Pages = {1586-1594},
	Title = {Universal classification for hidden {Markov models}},
	Volume = {37},
	Year = {1991},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/18.104319}}

@article{wal43,
	Abstract = {Let $x_1,\cdots,x_r$ be $r$ random variables whose joint probability density function $f(x_1,\cdots,x_r,\theta_1,\cdots,\theta_k)$ is assumed known except for the values of the parameters $\theta_1,\cdots,\theta_k$. The author considers the general problem of testing hypotheses about the values of $\theta_1,\cdots,\theta_k$ when the number of independent observations approaches infinity. A hypothesis $H_\omega$ that the point $\theta=\theta_1,\cdots,\theta_k$ lies in a given subset $\omega$ of the parameter space $\Omega$ is tested on the basis of $n$ independent observations on $x_1,\cdots,x_r$ as follows. A critical region (subset) $W_n$ of the $rn$-dimensional sample space is chosen and the hypothesis is rejected if and only if the observed sample point lies in the critical region $W_n$.Let $P(W_n|\theta)$ denote the probability that the sample point will fall in $W_n$ when $\theta$ is the parameter point. The author considers the following three definitions of ``best'' critical regions. (I) Let $F$ be a given family of surfaces in the parameter space such that each element of $F$ lies entirely in the complement $\overline\omega$ of $\omega$. Let $w(\theta)$ be a given nonnegative ``weight'' function defined over the entire parameter space. A critical region $W_n$ is said to have uniformly best average power with respect to the family $F$ of surfaces and the weight function $w(\theta)$ if $$ \int_{F_0}P(W_n|\theta)w(\theta)dA\geq\int_{F_0}P(Z_n|\theta)w(\theta)dA $$ for any element $F_0$ of $F$ and for any region $Z_n$ of the $rn$-dimensional sample space for which $$ \underset\theta\in\omega\to{\text{l.u.b.}}P(Z_n|\theta)=\underset\theta\in\omega\to{\text{l.u.b.}}P(W_n|\theta). $$ (II) Let $F$ be as before. A critical region $W_n$ for testing $H_\omega$ is said to have uniformly best constant power on the family $F$ if (a) $P(W_n|\theta)$ is constant over each element of $F$; (b) if $Z_n$ satisfies (a) and the condition $$ \underset\theta\in\omega\to{\text{l.u.b.}}P(Z_n|\theta)=\underset\theta\in\omega\to{\text{l.u.b.}}P(W_n|\theta), $$ then $P(W_n|\theta)\geq P(Z_n|\theta)$ for any $\theta$ not in $\omega$. (III) Denote by $P_n(\theta,\omega,\alpha)$ the l.u.b. of $P(Z_n|\theta)$ with respect to $Z_n$ subject to the condition that $\text{l.u.b.}_{\theta\in\omega}P(Z_n|\theta)=\alpha$, a preassigned constant. A critical region $W_n$ is said to give a most stringent test of $H_\omega$ if, for some positive $\alpha$, $\text{l.u.b.}_{\theta\in\omega}P(W_n|\theta)=\alpha$ and $$ \underset\theta\in\overline\omega\to{\text{l.u.b.}}\,{P_n(\theta,\omega,\alpha)-P(W_n|\theta)\}\leq\underset\theta\in\overline\omega\to{\text{l.u.b.}}\,{P_n(\theta,\omega,\alpha)-P(Z_n|\theta)} $$ for all regions $Z_n$ for which $\text{l.u.b.}_{\theta\in\omega}P(Z_n|\theta)=\alpha$.

One of the main results obtained is the following. Under certain restrictions on the density function $f$ and on $H_\omega$ the Neyman-Pearson likelihood ratio test is asymptotically ``best'' in the sense of each of the three definitions. The family $F$ and weight function $w(\theta)$ with respect to which the likelihood ratio test has asymptotically best average and asymptotically best constant power are of relatively simple structure. The author also derives the limiting form of the power function of the likelihood ratio test when the number of observations approaches infinity.
Reviewed by J. Wolfowitz
},
	Author = {Wald, Abraham},
	Date-Added = {2009-07-08 07:02:01 -0400},
	Date-Modified = {2009-07-08 07:02:01 -0400},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {62.0X},
	Mrnumber = {MR0012401 (7,20i)},
	Mrreviewer = {J. Wolfowitz},
	Pages = {426--482},
	Title = {Tests of statistical hypotheses concerning several parameters when the number of observations is large},
	Volume = {54},
	Year = {1943}}

@article{wil38,
	Author = {Wilks, S. S.},
	Date-Added = {2009-07-08 07:01:43 -0400},
	Date-Modified = {2009-07-08 07:01:43 -0400},
	Fjournal = {Annals of Mathematical Statistics},
	Journal = {Ann. Math. Statistics},
	Pages = {60--62},
	Title = {The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses},
	Volume = {9},
	Year = {1938}}

@book{wil62,
	Abstract = {important book is, in the author's own words, intended to introduce mathematical statistics to readers with good undergraduate backgrounds in mathematics. In the reviewer's opinion, it is hardly an introductory book, but certainly an excellent text-book on an advanced level, and most likely to become a valuable source of reference for research workers in theoretical as well as applied statistics.

The following condensed list of the contents will give a general idea of the scope of the book: (1--5) Probabilistic prerequisites: probability measures, distribution functions, means and moments, random sequences, characteristic functions; (6--7) Special distributions; (8--9) Sampling theory: exact and asymptotic; (10--11) Estimation: linear, nonparametric, parametric; (13--14) Testing parametric and nonparametric hypotheses; (15) Sequential analysis; (16) Decision functions; (17) Time series; (18) Multivariate statistical theory.

No less than 411 exercises are offered; they are largely selected from original papers and partly serve to introduce additional material. There are nineteen pages of references at the end of the book, and plenty of bibliographical information in the text.

As the author states in his preface, he has tried to make a unified and systematic presentation of classical results of mathematical statistics, without going into too many ramifications. This he has accomplished with great skill. Among noteworthy features in the direction of systematization, the reviewer would like to mention the modern and stringent presentation in Chapters 1--5 of the fundamentals of probability; the theory of matrix sampling and of coverage distributions in Chapter 8; the method of randomization in Chapter 14; the brief and helpful introduction to spectral theory in Chapter 17; and the multivariate theory in Chapter 18, where the notion of scatter plays a unifying role.---The reader also finds many interesting pieces of knowledge from outside the beaten track, e.g., the finite-population version of many sampling problems; Hoeffding's results on symmetric functions of a sample; Halmos's symmetry argument for minimum variance estimators; the exact combinatorial formulas of Birnbaum and Tingey, Massey, Gnedenko and Korolink in the theory of confidence contours and confidence bands.

In view of the author's professed intention to make a selection in accordance with his own preferences and prejudices, it will be no criticism, but rather a piece of information for the reader, to list a few topics that could perhaps have been treated differently or more thoroughly. Experimental design receives very little attention. There is no mention of estimation by linear combination of order statistics. The common matrix and vector notation and ready-made matrix manipulations are used very little. The somewhat heavy multiparametric estimation and testing theory could have been made more intuitive through reference to the previously treated linear situation. In accordance with the general conservative program of the book, decision theory receives only a brief chapter.

The concise style, the carefully chosen notation, and the emphasis on mathematical methods, as opposed to statistical techniques, remind the reader of Cram{\'e}r's classical book [Mathematical methods of statistics,\/ Princeton Univ. Press, Princeton, N.J., 1946; MR0016588 (8,39f)]. The author has more material and somewhat less philosophy. The details are sometimes complex; the totality is of appealing simplicity and homogeneity. },
	Address = {New York},
	Author = {Wilks, Samuel S.},
	Date-Added = {2009-07-08 06:59:36 -0400},
	Date-Modified = {2009-07-08 06:59:36 -0400},
	Mrclass = {62.00},
	Mrnumber = {MR0144404 (26 \#1949)},
	Mrreviewer = {G. Elfving},
	Pages = {xvi+644},
	Publisher = {John Wiley \& Sons Inc.},
	Series = {{A Wiley Publication in Mathematical Statistics}},
	Title = {Mathematical statistics},
	Year = {1962}}

@misc{konmey09a,
	Author = {I. Kontoyiannis and S. P. Meyn},
	Date-Added = {2009-07-05 13:25:32 -0400},
	Date-Modified = {2009-12-04 08:33:11 -0600},
	Howpublished = {http://arxiv.org/abs/0906.0259, and submitted for publication.},
	Month = {June},
	Title = {Approximating a Diffusion by a {Hidden {Markov} Model}},
	Year = {2009},
	Bdsk-Url-1 = {http://arxiv.org/abs/0906.0259}}

@misc{konmey09b,
	Author = {I. Kontoyiannis and S. P. Meyn},
	Date-Added = {2009-07-05 13:25:32 -0400},
	Date-Modified = {2009-12-06 11:41:58 -0600},
	Howpublished = {http://arxiv.org/abs/0906.5322},
	Month = {June},
	Title = {Geometric Ergodicity and the Spectral Gap of Non-Reversible {Markov} Chains},
	Year = {2009},
	Bdsk-Url-1 = {http://arxiv.org/abs/0906.5322}}

@techreport{clabar89,
	Author = {Clarke, B. and Barron, A. R.},
	Date-Added = {2009-06-30 13:58:56 -0500},
	Date-Modified = {2009-06-30 13:58:56 -0500},
	Institution = {Univ. of Illinois, Department of Statistics},
	Month = {July},
	Number = {26},
	Title = {Information theoretic asymptotics of Bayes' methods},
	Type = {Tech. Rep.},
	Year = {1989}}

@article{csishi04,
	Author = {Imre Csisz{\'a}r and Paul C. Shields},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-06-30 13:49:02 -0500},
	Date-Modified = {2009-06-30 13:49:02 -0500},
	Ee = {http://dx.doi.org/10.1561/0100000004},
	Journal = {Foundations and Trends in Communications and Information Theory},
	Number = {4},
	Title = {Information Theory and Statistics: A Tutorial},
	Volume = {1},
	Year = {2004}}

@incollection{tod07,
	Address = {Cambridge, MA},
	Author = {Emanuel Todorov},
	Booktitle = {Advances in Neural Information Processing Systems 19},
	Date-Added = {2009-06-29 16:46:36 -0500},
	Date-Modified = {2009-06-29 16:46:36 -0500},
	Editor = {B. Sch\"{o}lkopf and J. Platt and T. Hoffman},
	Pages = {1369--1376},
	Publisher = {MIT Press},
	Title = {Linearly-solvable {Markov} decision problems},
	Year = {2007}}

@article{kapgomopp09,
	Author = {B. Kappen and V. Gomez and M. Opper},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-06-29 16:45:58 -0500},
	Date-Modified = {2009-06-29 16:45:58 -0500},
	Ee = {http://arxiv.org/abs/0901.0633},
	Journal = {CoRR},
	Title = {Optimal control as a graphical model inference problem},
	Volume = {abs/0901.0633},
	Year = {2009}}

@article{kap05,
	Author = {Kappen, H. J.},
	Date-Added = {2009-06-24 15:25:01 -0500},
	Date-Modified = {2009-06-24 15:25:15 -0500},
	Doi = {10.1103/PhysRevLett.95.200201},
	Journal = {Phys. Rev. Lett.},
	Month = {Nov},
	Number = {20},
	Numpages = {4},
	Pages = {200201},
	Publisher = {American Physical Society},
	Title = {Linear Theory for Control of Nonlinear Stochastic Systems},
	Volume = {95},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.95.200201}}

@article{dia09,
	Author = {Diaconis, P.},
	Coden = {BAMOAD},
	Date-Added = {2009-06-01 18:21:22 -0500},
	Date-Modified = {2009-06-01 18:21:22 -0500},
	Fjournal = {American Mathematical Society. Bulletin. New Series},
	Issn = {0273-0979},
	Journal = {Bull. Amer. Math. Soc. (N.S.)},
	Mrclass = {60J20 (65C05)},
	Mrnumber = {MR2476411},
	Number = {2},
	Pages = {179--205},
	Title = {The {M}arkov chain {M}onte {C}arlo revolution},
	Volume = {46},
	Year = {2009}}

@article{guileowuyao09,
	Author = {Guillin, A. and L\'{e}onard, C. and Wu, L. and Yao, N.},
	Date-Added = {2009-05-26 14:51:58 -0500},
	Date-Modified = {2009-05-26 14:52:22 -0500},
	Journal = PRF,
	Month = {July},
	Number = {3},
	Pages = {669--695},
	Priority = {2},
	Title = {Transportation-information inequalities for {Markov} processes},
	Url = {http://dx.doi.org/10.1007/s00440-008-0159-5},
	Volume = {144},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00440-008-0159-5}}

@article{blu94,
	Author = {L. Blume},
	Date-Added = {2009-05-17 22:34:32 -0700},
	Date-Modified = {2009-05-17 22:34:32 -0700},
	Journal = {Games and Economic Behavior},
	Pages = {387--424},
	Title = {The Statistical Mechanics of Best-Response Strategy Revision},
	Volume = {5},
	Year = {1994}}

@article{blu93,
	Author = {Blume Lawrence E.},
	Date-Added = {2009-05-17 12:43:43 -0700},
	Date-Modified = {2009-05-17 12:43:43 -0700},
	Journal = {Games and Economic Behavior},
	Month = {July},
	Number = {3},
	Pages = {387-424},
	Title = {The Statistical Mechanics of Strategic Interaction},
	Url = {http://ideas.repec.org/a/eee/gamebe/v5y1993i3p387-424.html},
	Volume = {5},
	Year = 1993,
	Bdsk-Url-1 = {http://ideas.repec.org/a/eee/gamebe/v5y1993i3p387-424.html}}

@inproceedings{kealitsin01,
	Address = {San Francisco, CA, USA},
	Author = {Kearns, M. J. and Littman, M. L. and Singh, S. P.},
	Booktitle = {UAI '01: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence},
	Date-Added = {2009-05-17 12:39:43 -0700},
	Date-Modified = {2009-05-17 12:40:03 -0700},
	Isbn = {1-55860-800-1},
	Pages = {253--260},
	Publisher = {Morgan Kaufmann Publishers Inc.},
	Title = {Graphical Models for Game Theory},
	Year = {2001}}

@incollection{darkau97,
	Abstract = {
We propose a method for modelling economic systems in which outcomes depend locally on the predictions that agents make of other agents. We develop populations games in which each agent adaptively searches for a good model of its environment. We demonstrate that such systems can exhibit persistent dynamics, cyclic oscillations between low and high complexity states, and other complex, yet endogenous, phenomena. We propose that these `adaptively rational' agents as a natural extension of rational expectations, suitable when mutual consistency is not realistic. We discuss the connections between our work and the programs of bounded rationality, evolutionary game theory, and models motivated by statistical mechanics.},
	Address = {Reading, MA},
	Author = {V. M. Darley and S. A. Kauffman},
	Booktitle = {{The Economy as an Evolving Complex System II}},
	Date-Added = {2009-05-17 12:32:43 -0700},
	Date-Modified = {2009-05-17 12:34:01 -0700},
	Editor = {W. B. Arthur, S. Durlaf, and D. Lane},
	Publisher = {Addison-Wesley},
	Title = {Natural Rationality},
	Year = {1997}}

@article{bromeyweb97,
	Author = {L. J. Brown and S. P. Meyn and R. A. Weber},
	Date-Added = {2009-05-11 08:43:26 -0500},
	Date-Modified = {2009-05-11 08:43:48 -0500},
	Journal = {IEEE Transactions on Control Systems Technology},
	Pages = {335--349},
	Title = {Adaptive Dead-Time Compensation with Application to a Robotic Welding System},
	Volume = {6},
	Year = {1997}}

@article{altlewabu07,
	Author = {Al-Tamimi, A. and Lewis, F. L. and Abu-Khalaf, M.},
	Date-Added = {2009-05-06 16:33:05 -0500},
	Date-Modified = {2009-05-06 16:34:51 -0500},
	Doi = {http://dx.doi.org/10.1016/j.automatica.2006.09.019},
	Issn = {0005-1098},
	Journal = {Automatica},
	Number = {3},
	Pages = {473--481},
	Title = {Brief paper: Model-free {Q}-learning designs for linear discrete-time zero-sum games with application to {H}-infinity control},
	Volume = {43},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.automatica.2006.09.019}}

@article{hag06a,
	Author = {H{\"a}ggstr{\"o}m, O.},
	Coden = {PTRFEU},
	Date-Added = {2009-05-05 10:27:41 -0500},
	Date-Modified = {2009-05-05 10:27:41 -0500},
	Issn = {0178-8051},
	Journal = PRF,
	Mrclass = {60J05 (60F05)},
	Number = {3},
	Pages = {470},
	Title = {Acknowledgement of priority concerning ``{O}n the central limit theorem for geometrically ergodic {M}arkov chains'' [{P}robab. {T}heory {R}elated {F}ields {\bf 132} (2005), no. 1, 74--82; MR2136867]},
	Volume = {135},
	Year = {2006}}

@article{bra83,
	Author = {Bradley, Jr., R. C.},
	Coden = {RMJMAE},
	Date-Added = {2009-05-05 10:27:41 -0500},
	Date-Modified = {2009-05-05 10:27:41 -0500},
	Fjournal = {The Rocky Mountain Journal of Mathematics},
	Issn = {0035-7596},
	Journal = {Rocky Mountain J. Math.},
	Mrclass = {60G10 (60F05)},
	Number = {1},
	Pages = {77--97},
	Title = {Information regularity and the central limit question},
	Volume = {13},
	Year = {1983}}

@article{choliu68,
	Author = {Chow, C. K. and Liu, C. N.},
	Date-Added = {2009-05-04 20:56:10 -0500},
	Date-Modified = {2009-05-04 20:56:10 -0500},
	Journal = TIT,
	Number = {3},
	Pages = {462-467},
	Title = {Approximating discrete probability distributions with dependence trees},
	Volume = {14},
	Year = {1968}}

@book{waijor08,
	Abstract = {The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances-including the key problems of computing marginals and modes of probability distributions-are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, Graphical Models, Exponential Families and Variational Inference develops general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. It describes how a wide variety of algorithms- among them sum-product, cluster variational methods, expectation-propagation, mean field methods, and max-product-can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to {Markov} chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.},
	Address = {Hanover, MA, USA},
	Author = {Wainwright, M. J. and Jordan, M. I.},
	Date-Added = {2009-04-30 08:01:05 -0500},
	Date-Modified = {2009-04-30 08:01:48 -0500},
	Isbn = {1601981848, 9781601981844},
	Publisher = {Now Publishers Inc.},
	Title = {Graphical Models, Exponential Families, and Variational Inference},
	Year = {2008}}

@article{clabar90,
	Author = {Clarke, Bertrand S. and Barron, Andrew R.},
	Coden = {IETTAW},
	Date-Added = {2009-04-29 21:07:41 -0500},
	Date-Modified = {2009-04-29 21:07:41 -0500},
	Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
	Issn = {0018-9448},
	Journal = {IEEE Trans. Inform. Theory},
	Mrclass = {62B10 (62C10)},
	Mrnumber = {MR1053841 (91a:62011)},
	Number = {3},
	Pages = {453--471},
	Title = {Information-theoretic asymptotics of {B}ayes methods},
	Volume = {36},
	Year = {1990}}

@book{douast99,
	Address = {Bellingham, WA},
	Date-Added = {2009-04-29 20:18:37 -0500},
	Date-Modified = {2009-04-29 20:18:37 -0500},
	Editor = {Dougherty, Edward R. and Astola, Jaakko T.},
	Isbn = {0-8194-3033-1; 0-7803-5385-4},
	Mrclass = {68U10 (94A08)},
	Mrnumber = {MR1721647 (2000k:68169)},
	Mrreviewer = {Gilbert Crombez},
	Pages = {xvi+453},
	Publisher = {SPIE Optical Engineering Press},
	Series = {SPIE/IEEE Series on Imaging Science \& Engineering},
	Title = {Nonlinear filters for image processing},
	Year = {1999}}

@book{tan96,
	Address = {Berlin},
	Author = {Tanizaki, Hisashi},
	Date-Added = {2009-04-29 20:18:37 -0500},
	Date-Modified = {2009-04-29 20:18:37 -0500},
	Edition = {Second},
	Isbn = {3-540-61326-9},
	Mrclass = {93-02 (93C10 93E11)},
	Mrnumber = {MR1422253 (97g:93006)},
	Note = {Estimation and applications},
	Pages = {xx+254},
	Publisher = {Springer-Verlag},
	Title = {Nonlinear filters},
	Year = {1996}}

@article{lanmey05,
	Abstract = {Web information retrieval is significantly more challenging than traditional well-controlled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Web's hyperlink structure. This structure has been exploited by several of today's leading Web search engines, particularly Google and Teoma. In this survey paper, we focus on Web information retrieval methods that use eigenvector computations, presenting the three popular methods of HITS, PageRank, and SALSA.},
	Author = {Langville, A. N. and Meyer, C. D.},
	Date-Added = {2009-04-28 08:46:42 -0500},
	Date-Modified = {2009-04-28 08:47:18 -0500},
	Fjournal = {SIAM Review},
	Issn = {0036-1445},
	Journal = {SIAM Rev.},
	Mrclass = {68P20 (15A18)},
	Mrnumber = {MR2149104 (2006a:68027)},
	Number = {1},
	Pages = {135--161 (electronic)},
	Title = {A survey of eigenvector methods for {Web} information retrieval},
	Volume = {47},
	Year = {2005}}

@article{konram08,
	Abstract = {The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous {Markov} chains and hidden {Markov} chains, and an extremal property associated with their martingale difference bounds is established. This work complements and generalizes certain concentration inequalities obtained by Marton and Samson, while also providing different proofs of some known results.
Primary Subjects: 60E15
Secondary Subjects: 60J10, 60G42},
	Author = {Kontorovich, Leonid and Ramanan, Kavita},
	Coden = {APBYAE},
	Date-Added = {2009-04-28 07:02:11 -0500},
	Date-Modified = {2009-04-28 07:02:59 -0500},
	Fjournal = {The Annals of Probability},
	Issn = {0091-1798},
	Journal = {Ann. Probab.},
	Keywords = {Concentration inequality; McDiarmid's bound; bounded martingale differences; {Markov} chains; contracting {Markov} chains; hidden {Markov} chains; mixing coefficients},
	Mrclass = {60E15 (60G42 60J10)},
	Mrnumber = {MR2478678},
	Number = {6},
	Pages = {2126--2158},
	Title = {Concentration inequalities for dependent random variables via the martingale method},
	Volume = {36},
	Year = {2008}}

@article{rab89,
	Author = {Rabiner, L. R.},
	Date-Added = {2009-04-25 12:57:28 -0500},
	Date-Modified = {2009-04-25 12:57:28 -0500},
	Journal = {Proc. IEEE},
	Month = feb,
	Number = {2},
	Pages = {257-285},
	Title = {A Tutorial on Hidden {M}arkov Models and Selected Applications in Speech Recognition},
	Volume = {77},
	Year = {1989}}

@book{lju99,
	Address = {NJ, USA},
	Author = {Ljung, Lennart},
	Citeulike-Article-Id = {2418289},
	Date-Added = {2009-04-25 12:38:00 -0500},
	Date-Modified = {2009-04-25 12:38:00 -0500},
	Keywords = {dmoea\_fft\_cec2008},
	Posted-At = {2008-02-23 11:27:00},
	Priority = {2},
	Publisher = {Prentice-Hall Inc.},
	Title = {System Identification: Theory for the User},
	Year = {1999}}

@article{raorawmay03,
	Author = {Rao, C.V. and Rawlings, J.B. and Mayne, D.Q.},
	Date-Added = {2009-04-25 11:30:20 -0500},
	Date-Modified = {2009-04-25 11:30:20 -0500},
	Doi = {10.1109/TAC.2002.808470},
	Issn = {0018-9286},
	Journal = TAC,
	Keywords = {Kalman filters, asymptotic stability, discrete time systems, dynamic programming, filtering theory, nonlinear control systems, optimal control, state estimation asymptotic stability, bounded stability, constrained state estimation, deterministic framework, inequality constraints, moving horizon approximation, moving horizon approximations, nonlinear discrete-time systems, online optimization, state estimator design, sufficient conditions},
	Month = {Feb.},
	Number = {2},
	Pages = {246-258},
	Title = {Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations},
	Volume = {48},
	Year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/TAC.2002.808470}}

@inproceedings{han07,
	Author = {Hansen, E. A.},
	Booktitle = {AAAI},
	Crossref = {DBLP:conf/aaai/2007},
	Date-Added = {2009-04-24 14:53:51 -0500},
	Date-Modified = {2009-04-24 14:54:05 -0500},
	Pages = {1237-1242},
	Title = {Indefinite-Horizon {POMDPs} with Action-Based Termination},
	Year = {2007}}

@phdthesis{han98,
	Author = {Hansen, Eric Anton},
	Date-Added = {2009-04-24 14:53:27 -0500},
	Date-Modified = {2009-04-24 14:53:37 -0500},
	Isbn = {0-599-07332-2},
	Note = {Director: Zilberstein, Shlomo},
	School = {University of Massachusetts Amherst},
	Title = {Finite-memory control of partially observable systems},
	Year = {1998}}

@article{cosduf08,
	Address = {Philadelphia, PA, USA},
	Author = {Costa, O., L. V. and Dufour, F.},
	Date-Added = {2009-04-22 17:29:56 -0500},
	Date-Modified = {2009-04-22 17:30:05 -0500},
	Doi = {http://dx.doi.org/10.1137/060670109},
	Issn = {0363-0129},
	Journal = {SIAM J. Control Optim.},
	Number = {2},
	Pages = {1053--1077},
	Publisher = {Society for Industrial and Applied Mathematics},
	Title = {Stability and Ergodicity of Piecewise Deterministic {Markov} Processes},
	Volume = {47},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/060670109}}

@book{stechr08,
	Author = {Steinwart, I. and Christmann, A.},
	Date-Added = {2009-04-12 14:50:01 -0500},
	Date-Modified = {2009-04-12 14:50:37 -0500},
	Isbn = {0387772413},
	Publisher = {Springer Publishing Company},
	Title = {{Support Vector Machines}},
	Year = {2008}}

@article{nguwaijor08,
	Author = {Nguyen, X. and Wainwright, M. J. and Jordan, M. I.},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-04-12 14:19:09 -0500},
	Date-Modified = {2009-04-12 14:19:28 -0500},
	Ee = {http://arxiv.org/abs/0809.0853},
	Journal = {CoRR},
	Title = {Estimating divergence functionals and the likelihood ratio by convex risk minimization},
	Volume = {abs/0809.0853},
	Year = {2008}}

@phdthesis{swine05,
	Address = {Urbana, Illinois USA},
	Author = {El-Khatib, Firas Hasan A},
	Date-Added = {2009-03-20 10:12:23 -0500},
	Date-Modified = {2009-03-20 10:12:23 -0500},
	School = {University of Illinois at Urbana-Champaign},
	Title = {System identification and adaptive closed-loop glucose control in a type 1 diabetic swine model},
	Year = {2005}}

@article{joh07,
	Address = {Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA},
	Author = {Johannsen, F. W.},
	Date-Added = {2009-03-16 18:23:36 -0500},
	Date-Modified = {2009-03-16 18:23:36 -0500},
	Journal = {P.O. Electrical Engineers Journal},
	Title = {Waiting times and number of calls},
	Year = {1907}}

@inproceedings{hermou02,
	Address = {Big Sky, Montana},
	Author = {Herman, S. and Moulin, P.},
	Booktitle = {Proc. of the IEEE Aerospace Conf},
	Date-Added = {2009-03-16 13:00:16 -0500},
	Date-Modified = {2009-03-16 13:00:16 -0500},
	Pages = {1789--1808},
	Title = {A particle filtering approach to {FM}-band passive radar tracking and automatic target recognition},
	Year = {March 2002}}

@article{laixin08a,
	Author = {Lai, T.L. and Xing, H.},
	Date-Added = {2009-03-10 09:09:08 -0500},
	Date-Modified = {2009-03-10 09:09:08 -0500},
	Doi = {10.1109/CDC.2008.4739184},
	Issn = {0191-2216},
	Journal = {Decision and Control, 2008. CDC 2008. 47th IEEE Conference on},
	Keywords = {hidden {Markov} models, piecewise constant techniques, recursive filters, smoothing methods, statistical analysisadaptive control, array-CGH data analysis, cancer, computational property, estimation, genetic study, hidden {Markov} filtering approach, multiple change-point models, online detection, piecewise constant parameters, recursive filters, smoothers, statistical property, stochastic systems},
	Month = {Dec.},
	Pages = {1914-1919},
	Title = {A hidden {Markov} filtering approach to multiple change-point models},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2008.4739184}}

@article{mamakshw90,
	Author = {Ma, D.-J. and Makowski, A. M. and Shwartz, A.},
	Coden = {STOPB7},
	Date-Added = {2009-03-09 12:46:10 -0500},
	Date-Modified = {2009-03-09 12:46:19 -0500},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = {Stochastic Process. Appl.},
	Mrclass = {62L20 (60J10)},
	Mrnumber = {MR1062581 (92b:62117)},
	Number = {1},
	Pages = {27-45},
	Title = {Stochastic approximations for finite-state {M}arkov chains},
	Volume = {35},
	Year = {1990}}

@inproceedings{vraabulewwan07,
	Abstract = {Approximate dynamic programming has been formulated and applied mainly to discrete-time systems. Expressing the ADP concept for continuous-time systems raises difficult issues related to sampling time and system model knowledge requirements. In this paper is presented a novel online adaptive critic (AC) scheme, based on approximate dynamic programming (ADP), to solve the infinite horizon optimal control problem for continuous-time dynamical systems; thus bringing together concepts from the fields of computational intelligence and control theory. Only partial knowledge about the system model is used, as knowledge about the plant internal dynamics is not needed. The method is thus useful to determine the optimal controller for plants with partially unknown dynamics. It is shown that the proposed iterative ADP algorithm is in fact a quasi-Newton method to solve the underlying algebraic Riccati equation (ARE) of the optimal control problem. An initial gain that determines a stabilizing control policy is not required. In control theory terms, in this paper is developed a direct adaptive control algorithm for obtaining the optimal control solution without knowing the system A matrix},
	Author = {Vrabie, D. and Abu-Khalaf, M. and Lewis, F.L. and Wang, Y.},
	Booktitle = {Proc. IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning},
	Date-Added = {2009-02-22 16:14:52 -0600},
	Date-Modified = {2009-02-22 16:15:48 -0600},
	Doi = {10.1109/ADPRL.2007.368195},
	Keywords = {Riccati equations, adaptive control, continuous time systems, dynamic programming, infinite horizon, linear systems, optimal control, stabilityV-learning, adaptive control, algebraic Riccati equation, approximate dynamic programming, computational intelligence, continuous-time ADP, continuous-time dynamical systems, continuous-time systems, control theory, discrete-time systems, infinite horizon optimal control problem, linear systems, online adaptive critic scheme, partially unknown dynamics, policy iterations, quasiNewton method, sampling time, system model knowledge requirements},
	Month = {April},
	Pages = {247-253},
	Title = {Continuous-Time {ADP} for Linear Systems with Partially Unknown Dynamics},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ADPRL.2007.368195}}

@inproceedings{braydsbar94,
	Abstract = { In this paper we present the stability and convergence results for dynamic programming-based reinforcement learning applied to linear quadratic regulation (LQR). The specific algorithm we analyze is based on Q-learning and it is proven to converge to an optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. This is the first convergence result for DP-based reinforcement learning algorithms for a continuous problem.},
	Author = {Bradtke, S.J. and Ydstie, B.E. and Barto, A.G.},
	Booktitle = {{Proceedings of the 1994 American Control Conference}},
	Date-Added = {2009-02-22 15:56:02 -0600},
	Date-Modified = {2009-02-22 15:56:56 -0600},
	Doi = {10.1109/ACC.1994.735224},
	Keywords = {Adaptive control, discrete time systems, dynamic programming, intelligent control, iterative methods, learning (artificial intelligence), linear quadratic control, multivariable systems, stability Q-learning, adaptive linear quadratic control, convergence, discrete time systems, dynamic programming-based reinforcement learning, multivariable system, optimal controller, policy iteration, signal vector, stability},
	Pages = {3475-3479},
	Title = {Adaptive linear quadratic control using policy iteration},
	Volume = {3},
	Year = {1994},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ACC.1994.735224}}

@phdthesis{landelius97,
	Address = {SE-581 83 Link\"oping, Sweden},
	Author = {Landelius, T.},
	Date-Added = {2009-02-22 15:54:25 -0600},
	Date-Modified = {2009-02-22 15:54:25 -0600},
	Http = {http://www.imt.liu.se/mi/Publications/papers/landelius97.html},
	Note = {Dissertation No 469, ISBN 91-7871-892-9},
	School = {Link\"oping University, Sweden},
	Title = {{R}einforcement {L}earning and {D}istributed {L}ocal {M}odel {S}ynthesis},
	Year = {1997}}

@article{vrapasabulew09,
	Abstract = {
In this paper we propose a new scheme based on adaptive critics for finding online the state feedback, infinite horizon, optimal control solution of linear continuous-time systems using only partial knowledge regarding the system dynamics. In other words, the algorithm solves online an algebraic Riccati equation without knowing the internal dynamics model of the system. Being based on a policy iteration technique, the algorithm alternates between the policy evaluation and policy update steps until an update of the control policy will no longer improve the system performance. The result is a direct adaptive control algorithm which converges to the optimal control solution without using an explicit, a priori obtained, model of the system internal dynamics. The effectiveness of the algorithm is shown while finding the optimal-load-frequency controller for a power system.},
	Author = {Vrabie, D. and Pastravanu, O. and Abu-Khalaf, M. and Lewis, F.L.},
	Date-Added = {2009-02-22 15:47:34 -0600},
	Date-Modified = {2009-02-22 15:47:34 -0600},
	Doi = {DOI: 10.1016/j.automatica.2008.08.017},
	Issn = {0005-1098},
	Journal = {Automatica},
	Keywords = {LQR},
	Number = {2},
	Pages = {477 - 484},
	Title = {Adaptive optimal control for continuous-time linear systems based on policy iteration},
	Url = {http://www.sciencedirect.com/science/article/B6V21-4V7S8S4-1/2/4dc4175583049add149188c5abaa10bd},
	Volume = {45},
	Year = {2009},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V21-4V7S8S4-1/2/4dc4175583049add149188c5abaa10bd},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.automatica.2008.08.017}}

@article{huacaimal07,
	Abstract = {We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.},
	Author = {Huang, M. and Caines, P. E. and Malhame, R. P.},
	Date-Added = {2009-02-21 20:30:21 -0600},
	Date-Modified = {2009-02-21 20:36:05 -0600},
	Journal = TAC,
	Keywords = {decentralized control, dynamic games, game theory},
	Number = {9},
	Pages = {1560--1571},
	Title = {Large-Population Cost-Coupled {LQG} Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized {{$\varepsilon$}-Nash} Equilibria},
	Volume = {52},
	Year = {2007}}

@article{jac68a,
	Abstract = {Second-variation methods for computing optimal control exhibit more rapid convergence than first-variation methods but at the exponse of vastly increased computing effort.

In this paper two second-order algorithms for determining optimal control are derived using the notion of differential dynamic programming, which is also used to re-derive the well known second-variation method. This unified treatment allows the differences between the three algorithms to be studied in detail.

It is shown that the second-order algorithms are more accurate than the second-variation method and, moreover, that one of these algorithms is simpler to implement.
},
	Author = {Jacobson, D. H.},
	Date-Added = {2009-02-08 10:48:36 -0600},
	Date-Modified = {2009-02-08 10:48:48 -0600},
	Journal = {International J. of Control},
	Number = {6},
	Pages = {175-196},
	Title = {Second-order and Second-variation Methods for Determining Optimal Control: A Comparative Study using Differential Dynamic Programming},
	Volume = {7},
	Year = {1968}}

@unpublished{hanvan09,
	Author = {Han, J. and Van Roy, B.},
	Date-Added = {2009-02-08 07:40:39 -0600},
	Date-Modified = {2009-02-16 08:18:36 -0600},
	Note = {To appear in a volume on stochastic programming in honor of {George Dantzig}, edited by {Gerd Infanger}. Preprint available at http://www.stanford.edu/\~{ }bvr/},
	Title = {Control of Diffusions via Linear Programming},
	Year = {2009}}

@phdthesis{jac67,
	Address = {London, England},
	Author = {Jacobson, D. H.},
	Date-Added = {2009-02-08 07:23:57 -0600},
	Date-Modified = {2009-02-08 07:26:54 -0600},
	Keywords = {Dynamic programming, Nonlinear systems},
	School = {University of London},
	Title = {Differential dynamic programming methods for determining optimal control of non-linear systems},
	Year = {1967}}

@article{jac68,
	Author = {Jacobson, D. H.},
	Date-Added = {2009-02-08 07:23:57 -0600},
	Date-Modified = {2009-02-08 07:27:02 -0600},
	Issn = {0018-9286},
	Journal = TAC,
	Keywords = {Bang-bang control, Dynamic programming, Nonlinear systems},
	Month = {Dec},
	Number = {6},
	Pages = {661-675},
	Title = {Differential dynamic programming methods for solving bang-bang control problems},
	Volume = {13},
	Year = {1968}}

@book{jacmay70,
	Address = {New York, NY},
	Author = {Jacobson, D. H. and Mayne, D. Q.},
	Date-Added = {2009-02-07 12:41:14 -0600},
	Date-Modified = {2009-02-07 12:44:28 -0600},
	Isbn = {444000704},
	Pages = {208 p.},
	Publisher = {American Elsevier Pub. Co.},
	Subjects = {Control theory; Mathematical optimization; Dynamic programming},
	Title = {Differential dynamic programming},
	Year = {1970}}

@article{tasere07,
	Author = {Tassa, Y. and Erez, T.},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Date-Added = {2009-02-07 12:33:03 -0600},
	Date-Modified = {2009-02-07 12:33:45 -0600},
	Ee = {http://doi.ieeecomputersociety.org/10.1109/TNN.2007.899249},
	Journal = {IEEE Transactions on Neural Networks},
	Number = {4},
	Pages = {1031-1041},
	Title = {Least Squares Solutions of the {HJB} Equation With Neural Network Value-Function Approximators},
	Volume = {18},
	Year = {2007}}

@article{efehouluo06,
	Abstract = {We study the preconditioning of {Markov} chain Monte Carlo (MCMC) methods using coarse-scale models with applications to subsurface characterization. The purpose of preconditioning is to reduce the fine-scale computational cost and increase the acceptance rate in the MCMC sampling. This goal is achieved by generating {Markov} chains based on two-stage computations. In the first stage, a new proposal is first tested by the coarse-scale model based on multiscale finite volume methods. The full fine-scale computation will be conducted only if the proposal passes the coarse-scale screening. For more efficient simulations, an approximation of the full fine-scale computation using precomputed multiscale basis functions can also be used. Compared with the regular MCMC method, the preconditioned MCMC method generates a modified {Markov} chain by incorporating the coarse-scale information of the problem. The conditions under which the modified {Markov} chain will converge to the correct posterior distribution are stated in the paper. The validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed. We would like to note that coarse-scale models used in the simulations need to be inexpensive but not necessarily very accurate, as our analysis and numerical simulations demonstrate. We present numerical examples for sampling permeability fields using two-point geostatistics. The Karhunen-Lo{\`e}ve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data, such as production data, as well as some static data. Our numerical examples show that the acceptance rate can be increased by more than 10 times if MCMC simulations are preconditioned using coarse-scale models.'},
	Author = {Efendiev, Y. and Hou, T. and Luo, W.},
	Date-Added = {2009-01-27 20:12:43 -0600},
	Date-Modified = {2009-01-27 20:13:28 -0600},
	Fjournal = {SIAM Journal on Scientific Computing},
	Issn = {1064-8275},
	Journal = {SIAM J. Sci. Comput.},
	Mrclass = {65C05 (62F15 65C40 76M35 76S05)},
	Mrnumber = {MR2231730 (2007b:65009)},
	Mrreviewer = {Peter A. Lachenbruch},
	Number = {2},
	Pages = {776--803 (electronic)},
	Title = {Preconditioning {M}arkov chain {M}onte {C}arlo simulations using coarse-scale models},
	Volume = {28},
	Year = {2006},
	Bdsk-File-1 = {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}}

@article{farroy06,
	Abstract = {We introduce a new algorithm based on linear programming for optimization of average-cost {Markov} decision processes (MDPs). The algorithm approximates the differential cost function of a perturbed MDP via a linear combination of basis functions. We establish a bound on the performance of the resulting policy that scales gracefully with the number of states without imposing the strong Lyapunov condition required by its counterpart in de Farias and Van Roy [de Farias, D. P., B. Van Roy. 2003. The linear programming approach to approximate dynamic programming. Oper. Res.51(6) 850--865]. We investigate implications of this result in the context of a queueing control problem.},
	Address = {Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA},
	Author = {de Farias, D. P. Pucci and Van Roy, B.},
	Date-Added = {2009-01-25 06:56:18 -0600},
	Date-Modified = {2009-02-22 21:24:10 -0600},
	Doi = {http://dx.doi.org/10.1287/moor.1060.0208},
	Issn = {0364-765X},
	Journal = {Math. Oper. Res.},
	Number = {3},
	Pages = {597--620},
	Publisher = {INFORMS},
	Title = {A Cost-Shaping Linear Program for Average-Cost Approximate Dynamic Programming with Performance Guarantees},
	Volume = {31},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1287/moor.1060.0208}}

@article{meyhagmatban08,
	Abstract = {The purpose of this paper is to develop methods for model reduction for diffusion processes that exhibit cyclic behavior. For this purpose we extend techniques based on the spectral theory of {Markov} processes to the case of complex spectra. The main idea is to augment the state process for the diffusion with a clock process. For each complex eigenvalue for the original diffusion there exists a real eigenvalue for the augmented process. Results concerning metastability (or quasi-stationarity) are then applied to the augmented process. The results are illustrated through a linear diffusion, and an empirical model of combustion dynamics.},
	Author = {Meyn, S. P. and Hagen, G. and Mathew, G. and Banasuk, A.},
	Date-Added = {2009-01-09 08:15:13 -0600},
	Date-Modified = {2009-01-09 08:15:13 -0600},
	Doi = {10.1109/CDC.2008.4739211},
	Issn = {0191-2216},
	Journal = {Decision and Control, 2008. CDC 2008. 47th IEEE Conference on},
	Month = {Dec.},
	Pages = {3835-3839},
	Title = {On complex spectra and metastability of {Markov} models},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/CDC.2008.4739211}}

@article{krusmi98,
	Abstract = { How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative-agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross-sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior. },
	Author = {Krusell, P. and Smith Jr., A. A.},
	Date-Added = {2009-01-04 17:19:44 -0600},
	Date-Modified = {2009-01-04 17:19:44 -0600},
	Doi = {10.1086/250034},
	Eprint = {http://www.journals.uchicago.edu/doi/pdf/10.1086/250034},
	Journal = {Journal of Political Economy},
	Number = {5},
	Pages = {867-896},
	Title = {Income and Wealth Heterogeneity in the Macroeconomy},
	Url = {http://www.journals.uchicago.edu/doi/abs/10.1086/250034},
	Volume = {106},
	Year = {1998},
	Bdsk-Url-1 = {http://www.journals.uchicago.edu/doi/abs/10.1086/250034},
	Bdsk-Url-2 = {http://dx.doi.org/10.1086/250034}}

@inproceedings{konlasmey05a,
	Abstract = {We develop explicit, general bounds for the probability that the normalized partial sums of a function of a {Markov} chain on a general alphabet would exceed the steady-state mean of that function by a given amount. Our bounds combine simple information-theoretic ideas together with techniques from optimization and some fairly elementary tools from analysis. In one direction, we obtain a general bound for the important class of Doeblin chains; this bound is optimal, in the sense that in the special case of independent and identically distributed random variables it essentially reduces to the classical Hoeffding bound. In another direction, motivated by important problems in simulation, we develop a series of bounds in a form which is particularly suited to these problems, and which apply to the more general class of "geometrically ergodic" {Markov} chains},
	Author = {Kontoyiannis, I. and Lastras-Monta\~{n}o, L. A. and Meyn, S. P.},
	Booktitle = {Proc. of the {IEEE International Symposium on Information Theory}},
	Date-Added = {2009-01-02 07:18:24 -0600},
	Date-Modified = {2010-02-17 10:43:15 -0600},
	Doi = {10.1109/ISIT.2005.1523607},
	Keywords = {Markov processes, entropy, probabilityexponential deviation bounds, geometrically ergodic {Markov} chains, information-theoretic, probability, relative entropy},
	Month = {Sept.},
	Pages = {1563-1567},
	Title = {Relative entropy and exponential deviation bounds for general {Markov} chains},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ISIT.2005.1523607}}

@article{allblomeyperspo05,
	Abstract = { The existing US paradigm of individual departmental laboratories is increasingly difficult to justify due to the interdisciplinary nature of modern control engineering, the high cost and rapid obsolescence of technology, and the demands on faculty time. A shift from departmental labs to college labs is advocated for pedagogical, as well as financial, reasons. Because laboratories are a common resource to all departments, they can be funded at the college level and can be administered by faculty from the various engineering departments. This structure has been in place for ten years at Illinois and has proven to be an effective approach to undergraduate control systems education.},
	Author = {Alleyne, A.G. and Block, D.J. and Meyn, S.P. and Perkins, W.R. and Spong, M.W.},
	Date-Added = {2009-01-02 07:13:03 -0600},
	Date-Modified = {2009-01-02 07:13:03 -0600},
	Doi = {10.1109/MCS.2005.1388801},
	Issn = {0272-1708},
	Journal = {Control Systems Magazine, IEEE},
	Keywords = {control engineering education, laboratories, teaching college labs, individual departmental laboratories, interdisciplinary-interdepartmental control systems laboratory, modern control engineering, undergraduate control systems education},
	Month = {Feb.},
	Number = {1},
	Pages = {50-55},
	Title = {An interdisciplinary, interdepartmental control systems laboratory},
	Volume = {25},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/MCS.2005.1388801}}

@inproceedings{panmeyvee04,
	Abstract = { A robust hypothesis testing framework is introduced in which candidate hypotheses are characterized by moment classes. It is shown that there exists a test sequence that is asymptotically optimal in the min-max sense, and that it is expressed as a comparison of a log-linear combination of the constraint functions to a predetermined threshold.},
	Author = {Pandit, C. and Meyn, S. P. and Veeravalli, V.},
	Booktitle = {Proc. of the {IEEE International Symposium on Information Theory}},
	Date-Added = {2009-01-02 07:11:29 -0600},
	Date-Modified = {2010-02-17 10:42:53 -0600},
	Doi = {10.1109/ISIT.2004.1365255},
	Keywords = {binary sequences, minimax techniques, numerical analysis asymptotic robust Neyman-Pearson hypothesis testing, log-linear combination, min-max sense, moment class, test sequence},
	Month = {June-2 July},
	Pages = {220-},
	Title = {Asymptotic robust {Neyman-Pearson} hypothesis testing based on moment classes},
	Year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ISIT.2004.1365255}}

@article{yumehmey08,
	Abstract = {This paper is concerned with uncertainty based characterizations of fundamental performance limitations (Bode formula) and input-output properties (observability) in feedback systems. A hidden {Markov} model (HMM) formulation is introduced, based on which a belief process (conditional pdf) is defined. The belief process expresses uncertainty in the state conditioned on history of noisy observations. Both the Bode formula and observability are related to the asymptotic dynamics of the belief process. These results are described for the case of Gaussian linear systems and for open-loop nonlinear systems with negative Lyapunov exponents.},
	Author = {Sun, Y. and Mehta, P.G. and Meyn, S.},
	Date-Added = {2009-01-02 07:07:14 -0600},
	Date-Modified = {2009-01-02 07:08:00 -0600},
	Doi = {10.1109/ACC.2008.4586667},
	Issn = {0743-1619},
	Journal = {American Control Conference, 2008},
	Keywords = {Bode diagrams, Gaussian processes, Lyapunov methods, belief networks, feedback, hidden {Markov} models, linear systems, nonlinear control systems, observability, open loop systemsBode formula, Gaussian linear systems, Lyapunov exponents, belief propagation, feedback systems, hidden {Markov} model, observability, open-loop nonlinear system},
	Month = {June},
	Pages = {1268-1273},
	Title = {Belief propagation in feedback systems: Connections to {Bode} and observability},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ACC.2008.4586667}}

@book{bershr78,
	Address = {New York},
	Author = {Bertsekas, Dimitri P. and Shreve, Steven E.},
	Date-Added = {2008-12-29 12:36:59 -0600},
	Date-Modified = {2008-12-29 12:36:59 -0600},
	Isbn = {0-12-093260-1},
	Mrclass = {93E20},
	Mrnumber = {MR511544 (80d:93081)},
	Mrreviewer = {Vladimir Katkovnik},
	Note = {The discrete time case},
	Pages = {xiii+323},
	Publisher = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]},
	Series = {Mathematics in Science and Engineering},
	Title = {Stochastic optimal control},
	Volume = {139},
	Year = {1978}}

@book{bershr96a,
	Author = {Bertsekas, D.P. and Shreve, S.E.},
	Date-Added = {2008-12-29 12:36:07 -0600},
	Date-Modified = {2008-12-29 12:36:33 -0600},
	Publisher = {Athena Scientific},
	Title = {Stochastic Optimal Control: The Discrete-Time Case},
	Year = 1996}

@article{sut88,
	Address = {Hingham, MA, USA},
	Author = {Sutton, R. S.},
	Date-Added = {2008-12-29 08:22:54 -0600},
	Date-Modified = {2008-12-29 08:23:05 -0600},
	Doi = {http://dx.doi.org/10.1023/A:1022633531479},
	Issn = {0885-6125},
	Journal = {Mach. Learn.},
	Number = {1},
	Pages = {9--44},
	Publisher = {Kluwer Academic Publishers},
	Title = {Learning to Predict by the Methods of Temporal Differences},
	Volume = {3},
	Year = {1988},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1022633531479}}

@article{perbar03,
	Address = {Cambridge, MA, USA},
	Author = {Perkins, Theodore J. and Barto, Andrew G.},
	Date-Added = {2008-12-21 17:47:57 -0600},
	Date-Modified = {2008-12-21 17:48:09 -0600},
	Issn = {1533-7928},
	Journal = {{J. Mach. Learn. Res.}},
	Pages = {803--832},
	Publisher = {MIT Press},
	Title = {Lyapunov design for safe reinforcement learning},
	Volume = {3},
	Year = {2003}}

@phdthesis{wat89,
	Address = {Cambridge, UK},
	Author = {Watkins, C. J. C. H.},
	Date-Added = {2008-12-21 09:23:25 -0600},
	Date-Modified = {2008-12-21 09:23:33 -0600},
	School = {King's College},
	Title = {Learning from Delayed Rewards},
	Year = {1989}}

@unpublished{moakumvan08,
	Author = {Moallemi, C.C. and Kumar, S. and Van Roy, B.},
	Date-Added = {2008-12-21 09:19:54 -0600},
	Date-Modified = {2008-12-21 09:19:54 -0600},
	Note = {Preprint available at http://moallemi.com/ciamac/research-interests.php},
	Title = {Approximate and data-driven dynamic programming for queueing networks},
	Year = {2008}}

@book{kul97,
	Address = {Mineola, NY},
	Author = {Kullback, S.},
	Date-Added = {2008-12-19 08:29:34 -0600},
	Date-Modified = {2008-12-19 08:29:42 -0600},
	Note = {Reprint of the second (1968) edition},
	Publisher = {Dover Publications Inc.},
	Title = {Information Theory and Statistics},
	Year = {1997}}

@book{ris89,
	Address = {Singapore},
	Author = {Rissanen, J.},
	Date-Added = {2008-12-19 08:27:30 -0600},
	Date-Modified = {2008-12-19 08:28:03 -0600},
	Publisher = {World Scientific},
	Title = {Stochastic Complexity in Statistical Inquiry},
	Year = {1989}}

@unpublished{bormey08b,
	Author = {Borkar, V. and Meyn, S.},
	Date-Added = {2008-12-11 14:23:14 -0600},
	Date-Modified = {2011-01-11 04:45:37 -0600},
	Note = {Under revision for \textit{Automatica}.},
	Title = {Oja's Algorithm for Graph Clustering, {Markov} Spectral Decomposition, and Risk Sensitive Control},
	Year = {2008}}

@article{basbhabor08,
	Abstract = {A linear function approximation-based reinforcement learning algorithm is proposed for {Markov} decision processes with infinite horizon risk-sensitive cost. Its convergence is proved using the "o.d.e. method" for stochastic approximation. The scheme is also extended to continuous state space processes.
},
	Author = {Basu, A. and Bhattacharyya, T. and Borkar, V. S.},
	Date-Added = {2008-12-10 10:05:01 -0600},
	Date-Modified = {2008-12-10 10:06:35 -0600},
	Doi = {10.1287/moor.1080.0324},
	Eprint = {http://mor.journal.informs.org/cgi/reprint/33/4/880.pdf},
	Journal = MOR,
	Number = {4},
	Pages = {880-898},
	Title = {A Learning Algorithm for Risk-Sensitive Cost},
	Url = {http://mor.journal.informs.org/cgi/content/abstract/33/4/880},
	Volume = {33},
	Year = {2008},
	Bdsk-Url-1 = {http://mor.journal.informs.org/cgi/content/abstract/33/4/880},
	Bdsk-Url-2 = {http://dx.doi.org/10.1287/moor.1080.0324}}

@article{benman92,
	Author = {Bennett, K. and Mangasarian, O.},
	Date-Added = {2008-12-08 01:07:53 -0600},
	Date-Modified = {2008-12-08 01:07:53 -0600},
	Journal = {Optimization Methods and Software},
	Pages = {23--34},
	Title = {Robust linear programming discrimination of two linearly inseparable sets},
	Volume = {1},
	Year = {1992}}

@techreport{humancar08,
	Author = {Xu, Huan and Mannor, Shie and Caramanis, Constantine},
	Date-Added = {2008-12-08 00:59:29 -0600},
	Date-Modified = {2008-12-08 00:59:29 -0600},
	Institution = {McGill University},
	Title = {Robustness and Regularization of Support Vector Machines},
	Type = {Unpublished report},
	Year = {2008}}

@article{csi91,
	Author = {Csisz{\'{a}}r, I.},
	Date-Added = {2008-12-08 00:49:09 -0600},
	Date-Modified = {2008-12-08 00:49:09 -0600},
	Journal = ANNS,
	Pages = {2032--2066},
	Title = {Why Least Squares and Maximum Entropy? An Axiomatic Approach to Inference for Linear Inverse Problems},
	Volume = {19},
	Year = {1991}}

@article{bouboulug05,
	Author = {Boucheron, S. and Bousquet, O. and Lugosi, G.},
	Date-Added = {2008-12-08 00:38:42 -0600},
	Date-Modified = {2009-04-13 20:03:51 -0500},
	Doi = {10.1051/ps:2005018},
	Journal = {ESAIM: P\&S},
	Month = {nov},
	Pages = {323-375},
	Title = {Theory of Classification: a Survey of Some Recent Advances},
	Url = {http://dx.doi.org/doi/10.1051/ps:2005018},
	Volume = 9,
	Year = 2005,
	Bdsk-Url-1 = {http://dx.doi.org/doi/10.1051/ps:2005018},
	Bdsk-Url-2 = {http://dx.doi.org/10.1051/ps:2005018}}

@article{vapche64,
	Author = {Vapnik, V. and Chervonenkis, A.},
	Date-Added = {2008-12-06 19:04:22 -0600},
	Date-Modified = {2008-12-06 19:04:22 -0600},
	Journal = {Automat. Remote Control},
	Pages = {103--109},
	Title = {A note on a class of perceptrons},
	Volume = {25},
	Year = {1964}}

@unpublished{han08,
	Author = {Hansen, L. P.},
	Date-Added = {2008-12-03 20:22:55 -0600},
	Date-Modified = {2008-12-03 20:22:55 -0600},
	Note = {{NBER} working paper {\tt http://www.nber.org/papers/w14243}},
	Title = {Modeling the Long Run: Valuation in Dynamic Stochastic Economies},
	Year = {2008}}

@article{sch02,
	Author = {Schachermayer, W.},
	Date-Added = {2008-12-03 20:20:40 -0600},
	Date-Modified = {2008-12-03 20:20:40 -0600},
	Issue = {3},
	Journal = {Positivity},
	Pages = {359--368},
	Title = {No Arbitrage: On the Work of {David Kreps}},
	Volume = {6},
	Year = {2002}}

@article{robros97,
	Abstract = {Various notions of geometric ergodicity for {Markov} chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in {Markov} chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will &quot;inherit &quot; the geometric ergodicity of its constituent parts. Acknowledgements. We thank Charlie Geyer for a number of very useful comments regarding spectral theory and central limit theorems.  },
	Author = {Roberts, Gareth O. and Rosenthal, Jeffrey S.},
	Date-Added = {2008-11-23 13:28:23 -0600},
	Date-Modified = {2008-11-23 13:29:27 -0600},
	Journal = ECP,
	Pages = {13--25},
	Title = {Geometric ergodicity and hybrid {Markov} chains},
	Volume = {2},
	Year = {1997}}

@article{byrlin08,
	Author = {Byrnes, Christopher I. and Lindquist, Anders},
	Date-Added = {2008-11-03 16:05:58 -0600},
	Date-Modified = {2008-11-03 16:05:58 -0600},
	Doi = {10.1137/070693941},
	Journal = SICON,
	Keywords = {moment problems; interpolation; rational positive measures},
	Number = {5},
	Pages = {2458-2469},
	Publisher = {SIAM},
	Title = {Important Moments in Systems and Control},
	Url = {http://link.aip.org/link/?SJC/47/2458/1},
	Volume = {47},
	Year = {2008},
	Bdsk-Url-1 = {http://link.aip.org/link/?SJC/47/2458/1},
	Bdsk-Url-2 = {http://dx.doi.org/10.1137/070693941}}

@incollection{bor08b,
	Author = {Borkar, V. S.},
	Booktitle = {Perspectives in Mathematical Sciences},
	Date-Added = {2008-10-27 22:44:13 -0500},
	Date-Modified = {2008-12-10 10:07:38 -0600},
	Editor = {Sastry, N. S. N. and Rajeev, B. and Delampady, Mohan and Rao, T. S. S. R. K.},
	Publisher = {World Scientific},
	Title = {Reinforcement learning --- a bridge between numerical methods and {Markov Chain Monte Carlo}},
	Year = {2008}}

@article{bor02b,
	Abstract = {We propose for risk-sensitive control of finite {Markov} chains a counterpart of the popular Q-learning algorithm for classical {Markov} decision processes. The algorithm is shown to converge with probability one to the desired solution. The proof technique is an adaptation of the o.d.e. approach for the analysis of stochastic approximation algorithms, with most of the work involved used for the analysis of the specific o.d.e.s that arise.
},
	Author = {Borkar, V. S.},
	Date-Added = {2008-10-27 15:30:06 -0500},
	Date-Modified = {2008-10-28 08:53:07 -0500},
	Doi = {10.1287/moor.27.2.294.324},
	Eprint = {http://mor.journal.informs.org/cgi/reprint/27/2/294.pdf},
	Journal = MOR,
	Number = {2},
	Pages = {294-311},
	Title = {{$Q$}-Learning for Risk-Sensitive Control},
	Url = {http://mor.journal.informs.org/cgi/content/abstract/27/2/294},
	Volume = {27},
	Year = {2002},
	Bdsk-Url-1 = {http://mor.journal.informs.org/cgi/content/abstract/27/2/294},
	Bdsk-Url-2 = {http://dx.doi.org/10.1287/moor.27.2.294.324}}

@article{bor01,
	Author = {Borkar, V. S.},
	Date-Added = {2008-10-27 15:29:17 -0500},
	Date-Modified = {2008-10-27 15:29:42 -0500},
	Doi = {doi:10.1016/S0167-6911(01)00152-9},
	Journal = SCL,
	Pages = {339-346(8)},
	Title = {A sensitivity formula for risk-sensitive cost and the actor-critic algorithm},
	Url = {http://www.ingentaconnect.com/content/els/01676911/2001/00000044/00000005/art00152},
	Volume = {44},
	Year = {2001},
	Bdsk-Url-1 = {http://www.ingentaconnect.com/content/els/01676911/2001/00000044/00000005/art00152},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0167-6911(01)00152-9}}

@article{robros08,
	Abstract = {We introduce a new property of {Markov} chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis--Hastings algorithms.

},
	Author = {Roberts, G. O. and Rosenthal, J. S.},
	Date-Added = {2008-10-13 08:26:49 -0500},
	Date-Modified = {2008-10-13 08:26:57 -0500},
	Journal = ANNAP,
	Pages = {1201},
	Title = {Variance bounding {Markov} chains},
	Url = {doi:10.1214/07-AAP486},
	Volume = {18},
	Year = {2008},
	Bdsk-Url-1 = {doi:10.1214/07-AAP486}}

@inproceedings{isomeybra08,
	Address = {Chicago, IL},
	Author = {Isom, Joshua D. and Meyn, S. P. P. and Braatz, Richard D.},
	Booktitle = {23rd National Conference on Artificial Intelligence (AAAI-08)},
	Date-Added = {2008-09-01 08:25:29 -0500},
	Date-Modified = {2008-09-01 08:25:42 -0500},
	Pages = {291-197},
	Title = {Piecewise Linear Dynamic Programming for Constrained {POMDP}s},
	Year = {2008}}

@article{konmey08a,
	Arxiv = {math/0612040},
	Author = {Kontoyiannis, I. and Meyn, S. P.},
	Date-Added = {2008-08-25 07:05:55 -0500},
	Date-Modified = {2008-08-25 07:07:01 -0500},
	Doi = {10.1214/00-AAP492},
	Fjournal = {Annals of Applied Probability},
	Issn = {1050-5164},
	Journal = ANNAP,
	Number = {4},
	Pages = {1491-1518},
	Sici = {1050-5164(2008)18:4<1491:CEBFSE>2.0.CO;2-D},
	Title = {Computable exponential bounds for screened estimation and simulation},
	Volume = {18},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1214/00-AAP492}}

@inproceedings{barduasarwakbar05,
	Author = {Baron, D. and Duarte, M. F. and Sarvotham, S. and Wakin, M. B. and Baraniuk, R. G.},
	Booktitle = {Proc. 43rd Allerton Conf. Comm., Control, Comput.},
	Date-Added = {2008-08-24 12:17:40 -0500},
	Date-Modified = {2008-08-24 12:17:40 -0500},
	Month = {September},
	Title = {An Information-Theoretic Approach to Distributed Compressed Sensing},
	Year = {2005}}

@article{che01,
	Author = {Chen, Mu-Fa},
	Date-Added = {2008-08-21 16:11:04 -0700},
	Date-Modified = {2008-08-21 16:11:04 -0700},
	Fjournal = {Chinese Journal of Applied Probability and Statistics. Yingyong Gail\"u Tongji},
	Issn = {1001-4268},
	Journal = {Chinese J. Appl. Probab. Statist.},
	Mrclass = {60J80 (60J60)},
	Mrnumber = {MR1873761},
	Number = {2},
	Pages = {113--120},
	Title = {Explicit criteria for several types of ergodicity},
	Volume = {17},
	Year = {2001}}

@article{kra70,
	Author = {Krasulina, T. P.},
	Date-Added = {2008-07-26 22:20:06 -0400},
	Date-Modified = {2011-01-13 16:01:23 -0600},
	Journal = {Automat. Remote Control},
	Pages = {215--221},
	Title = {Method of stochastic approximation in the determination of the largest eigenvalue of the mathematical expectation of random matrices},
	Volume = {2},
	Year = {1970}}

@article{zouhas05,
	Author = {Zou, Hui and Hastie, Trevor},
	Date-Added = {2008-07-20 16:48:37 -0400},
	Date-Modified = {2008-07-20 16:48:37 -0400},
	Journal = {Journal Of The Royal Statistical Society Series B},
	Number = {2},
	Pages = {301-320},
	Title = {Regularization and variable selection via the elastic net},
	Url = {http://ideas.repec.org/a/bla/jorssb/v67y2005i2p301-320.html},
	Volume = {67},
	Year = 2005,
	Bdsk-Url-1 = {http://ideas.repec.org/a/bla/jorssb/v67y2005i2p301-320.html}}

@inbook{hastibfri01,
	Author = {Hastie, T. and Tibshirani, R. and Friedman, J.},
	Date-Added = {2008-07-20 14:24:55 -0400},
	Date-Modified = {2008-07-20 14:24:55 -0400},
	Edition = {Second},
	Note = {Corr. 3rd printing, 2003},
	Publisher = {Springer-Verlag},
	Series = {Springer Series in Statistics},
	Title = {The Elements of Statistical Learning},
	Year = {2001}}

@inproceedings{matbanmey08,
	Abstract = {Waveform Relaxation is a parallelizable iterative method for solving large scale 
nonlinear systems. At each iteration, the system is decomposed into several 
subsystems each of which is evolved forward in time independently but coupled 
with the other subsystems through their solutions from the previous iteration. 
We derive a convergence criteria that reveals the influence of the mutual in- 
teraction between the subsystems and self-interaction of each subsystem. We 
propose a decomposition of the system that allows for faster convergence of the 
waveform relaxation method. This decomposition is based on a graph derived 
from the Jacobian of the system.},
	Address = {Blacksburg, Virginia},
	Author = {Mathew, G. and Banaszuk, Andrzej and Meyn, S. P.},
	Booktitle = {Proceedings of the MTNS conference},
	Date-Added = {2008-07-11 13:56:11 -0500},
	Date-Modified = {2008-07-11 13:56:11 -0500},
	Title = {Waveform Relaxation and Graph Decomposition},
	Year = {2008}}

@book{mamell07,
	Address = {New York},
	Author = {Mamon, R. S. and Elliott, R. J.},
	Date-Added = {2008-07-07 19:45:08 -0500},
	Date-Modified = {2008-07-07 19:45:08 -0500},
	Publisher = {Springer-Verlag},
	Series = {International Series in Operations Research \&\ Management Science},
	Title = {Hidden {Markov} Models in Finance},
	Volume = {104},
	Year = 2007}

@book{feishw01,
	Address = {Holland},
	Date-Added = {2008-07-07 19:32:48 -0500},
	Date-Modified = {2008-07-07 19:36:35 -0500},
	Editor = {Feinberg, E. and Shwartz, A.},
	Publisher = {Kluwer Acad. Publ.},
	Title = {Markov Decision Processes: Models, Methods, Directions, and Open Problems},
	Year = {2001}}

@book{asmgly07,
	Address = {New York},
	Author = {Asmussen, S. and Glynn, P. W.},
	Date-Added = {2008-06-22 19:59:02 -0500},
	Date-Modified = {2008-06-22 19:59:02 -0500},
	Publisher = {Springer-Verlag},
	Series = {Stochastic Modelling and Applied Probability},
	Title = {Stochastic Simulation: Algorithms and Analysis},
	Volume = {57},
	Year = 2007}

@book{liuBook01,
	Address = {New York},
	Author = {Liu, J. S.},
	Date-Added = {2008-06-18 12:13:34 -0500},
	Date-Modified = {2008-06-18 12:13:59 -0500},
	Isbn = {0-387-95230-6},
	Mrclass = {65C05 (60J10 62F15 65D30 81-08 82C80)},
	Mrnumber = {MR1842342 (2002i:65006)},
	Mrreviewer = {Michael J. Evans},
	Pages = {xvi+343},
	Publisher = {Springer-Verlag},
	Series = {Springer Series in Statistics},
	Title = {Monte {C}arlo strategies in scientific computing},
	Year = {2001}}

@book{robcas04,
	Address = {New York},
	Author = {Robert, C. P. and Casella, G.},
	Date-Added = {2008-06-18 12:10:06 -0500},
	Date-Modified = {2008-06-18 12:10:19 -0500},
	Edition = {Second},
	Isbn = {0-387-21239-6},
	Mrclass = {62-01 (60J10 62F15 65Cxx)},
	Mrnumber = {MR2080278 (2005d:62006)},
	Mrreviewer = {Petru P. Blaga},
	Pages = {xxx+645},
	Publisher = {Springer-Verlag},
	Series = {Springer Texts in Statistics},
	Title = {Monte {C}arlo statistical methods},
	Year = {2004}}

@article{jarhan00,
	Author = {Jarner, S. F. and Hansen, S.},
	Coden = {STOPB7},
	Date-Added = {2008-06-18 12:08:04 -0500},
	Date-Modified = {2008-06-18 12:08:37 -0500},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = SPA,
	Mrclass = {60J05 (62F15 62P10)},
	Mrnumber = {MR1731030 (2001c:60108)},
	Mrreviewer = {Jean Diebolt},
	Number = {2},
	Pages = {341--361},
	Title = {Geometric ergodicity of {M}etropolis algorithms},
	Volume = {85},
	Year = {2000}}

@article{wu04,
	Abstract = { Let $P(x,dy)$ be a {Markov} transition kernel on some Polish space $E$. We also regard $P$ as an operator on some Banach lattice $\Bbb B$. The lattices considered in the paper are (1) the space of measurable bounded functions on $E$, (2) the space of continuous bounded functions on $E$, and (3) the $L\sp p$-space on $E$ for some $p\in(1,\infty)$ with respect to some invariant probability measure. The main object of interest in the paper is the essential radius, $$r\sb{\rm ess}(P|\sb {\Bbb B})=\sup\{|\lambda|\colon \lambda\in\sigma \sb{\rm ess}(P|\sb {\Bbb B})\},$$ where $\sigma\sb{\rm ess}(P)$ denotes the Wolff essential spectrum, the set of $\lambda\in\Bbb C$ such that $\lambda-P$ is not a Fredholm operator. If $P$ is irreducible and aperiodic, then we have $r\sb{\rm ess}(P|\sb {\Bbb B})<1$ if and only if $r\sb{\exp}(P|\sb {\Bbb B})<1$, where $r\sb{\exp}(P|\sb {\Bbb B})$ is the supremum over all $|\lambda|\not=1$ with $\lambda$ in the usual spectrum of $P|\sb {\Bbb B}$.

In pioneering work in the 1930s, Doeblin proved the following sufficient criterion in the case where $\Bbb B$ is the space of measurable bounded functions on $E$: If $\sup\sb {A\subset\Bbb B\colon \nu(A)<\eta}P\sp N(x,A)<1$, for some $N\in\Bbb N$ and for some probability measure $\nu$ on $E$ and some $\eta>0$, then $r\sb{\exp}(P|\sb {\Bbb B})<1$. Other sufficient criteria proved by Doeblin are in terms of upper estimates of $Pu/u$ for a bounded measurable function $u\colon E\to[1,\infty)$ (called a drift condition), and in terms of exponential moments of hitting times of compact subsets for the associated {Markov} chain (called the geometric recurrence condition).

In the present paper, estimates for $r\sb{\rm ess}(P|\sb {\Bbb B})$ are given in terms of the above-mentioned criteria and in terms of other related objects, like a weighted supremum norm and, in the case where $\Bbb B$ is an $L\sp p$-space, the drift condition with unbounded function $u$. The main tools are two new measures of non-compactness, $\beta\sb \tau(P)$ and $\beta\sb w(P)$, and a new formula of Nussbaum-Gel\cprime fand type for $r\sb{\rm ess}(P|\sb {\Bbb B})$. No irreducibility or aperiodicity of $P$ is assumed. Moreover, it is proved that the Donsker-Varadhan large deviation principle for the associated {Markov} chain holds if and only if the essential spectral radius is zero. Furthermore, eigenvalues of $P$ on $L\sb 2$-space in the symmetric case are estimated, and geometric convergence rates in the Wasserstein metric for the convergence towards equilibrium are estimated. Some concrete examples are given.
 },
	Author = {Wu, Liming},
	Coden = {PTRFEU},
	Date-Added = {2008-06-18 11:41:35 -0500},
	Date-Modified = {2008-06-18 11:42:54 -0500},
	Fjournal = {Probability Theory and Related Fields},
	Issn = {0178-8051},
	Journal = PRF,
	Mrclass = {60J05 (47A10 47D07 60F10)},
	Mrnumber = {MR2031227 (2005a:60110)},
	Mrreviewer = {Wolfgang K{\"o}nig},
	Number = {2},
	Pages = {255--321},
	Title = {Essential spectral radius for {M}arkov semigroups. {I}. {D}iscrete time case},
	Volume = {128},
	Year = {2004}}

@incollection{chilipvan08,
	Author = {Chigansky, P. and Liptser, R. and van Handel, R.},
	Booktitle = {Handbook of Nonlinear Filtering},
	Date-Added = {2008-06-14 06:40:32 -0700},
	Date-Modified = {2008-06-14 06:43:14 -0700},
	Note = {To appear},
	Publisher = {Oxford University Press},
	Title = {Intrinsic methods in filter stability},
	Year = {2008}}

@article{sco02,
	Author = {Scott, Steven L.},
	Date-Added = {2008-06-05 20:43:15 -0400},
	Date-Modified = {2008-06-05 20:43:15 -0400},
	Journal = {JASA},
	Pages = {337--351},
	Title = {Bayesian Methods for Hidden {Markov} Models:Recursive Computing in the 21st Century},
	Volume = {97},
	Year = {2002}}

@article{altavrkonnun04,
	Author = {Altman, Eitan and Avrachenkov, Konstantin E. and N{\'u}{\~n}ez-Queija, Rudesindo},
	Coden = {AAPBBD},
	Date-Added = {2008-05-22 20:37:03 -0500},
	Date-Modified = {2008-05-22 20:37:03 -0500},
	Fjournal = {Advances in Applied Probability},
	Issn = {0001-8678},
	Journal = {Adv. in Appl. Probab.},
	Mrclass = {60J10 (60J22 60J27 60K25)},
	Mrnumber = {MR2079917 (2005h:60210)},
	Mrreviewer = {Walter M. B{\"o}hm},
	Number = {3},
	Pages = {839--853},
	Title = {Perturbation analysis for denumerable {M}arkov chains with application to queueing models},
	Volume = {36},
	Year = {2004}}

@article{wuyao08,
	Author = {Wu, L. and Yao, N.},
	Date-Added = {2008-05-22 10:35:51 -0500},
	Date-Modified = {2008-05-22 10:40:51 -0500},
	Fjournal = {Electronic Communications in Probability},
	Issn = {1083-589X},
	Journal = {Electron. Commun. Probab.},
	Mrclass = {60F10},
	Mrnumber = {MR2372833},
	Pages = {10--23},
	Title = {Large deviation principles for {M}arkov processes via {$\Phi$}-{S}obolev inequalities},
	Volume = {13},
	Year = {2008},
	Bdsk-File-1 = {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}}

@article{lai94,
	Abstract = {Stochastic regression models of the form yi = fi(θ) + εi, where the random disturbances εi form a martingale difference sequence with respect to an increasing sequence of σ-fields {Gi} and fi is a random Gi - 1-measurable function of an unknown parameter θ, cover a broad range of nonlinear (and linear) time series and stochastic process models. Herein strong consistency and asymptotic normality of the least squares estimate of θ in these stochastic regression models are established. In the linear case fi(θ) = θTψi, they reduce to known results on the linear least squares estimate (∑n 1ψiψT i)-1∑n 1ψi yi with stochastic Gi - 1-measurable regressors ψi.},
	Author = {Lai, Tze Leung},
	Date-Added = {2008-05-21 18:05:10 -0500},
	Date-Modified = {2010-05-19 18:21:00 -0500},
	Issn = {00905364},
	Journal = {The Annals of Statistics},
	Jstor_Articletype = {primary_article},
	Number = {4},
	Pages = {1917--1930},
	Publisher = {Institute of Mathematical Statistics},
	Title = {Asymptotic Properties of Nonlinear Least Squares Estimates in Stochastic Regression Models},
	Url = {http://www.jstor.org/stable/2242491},
	Volume = {22},
	Year = {1994},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2242491}}

@article{laiwei82,
	Abstract = {Strong consistency and asymptotic normality of least squares estimates in stochastic regression models are established under certain weak assumptions on the stochastic regressors and errors. We discuss applications of these results to interval estimation of the regression parameters and to recursive on-line identification and control schemes for linear dynamic systems.},
	Author = {Lai, Tze Leung and Wei, Ching Zong},
	Copyright = {Copyright {\copyright} 1982 Institute of Mathematical Statistics},
	Date-Added = {2008-05-21 18:03:48 -0500},
	Date-Modified = {2008-05-21 18:03:48 -0500},
	Issn = {00905364},
	Journal = {The Annals of Statistics},
	Jstor_Articletype = {primary_article},
	Jstor_Formatteddate = {Mar., 1982},
	Number = {1},
	Pages = {154--166},
	Publisher = {Institute of Mathematical Statistics},
	Title = {Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems},
	Url = {http://www.jstor.org/stable/2240506},
	Volume = {10},
	Year = {1982},
	Bdsk-Url-1 = {http://www.jstor.org/stable/2240506}}

@article{fuhzha00,
	Author = {Fuh, Cheng-Der and Zhang, Cun-Hui},
	Coden = {STOPB7},
	Date-Added = {2008-05-20 18:23:06 -0500},
	Date-Modified = {2008-05-20 18:23:44 -0500},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = SPA,
	Mrclass = {60G40 (60J10)},
	Mrnumber = {MR1751164 (2002d:60031)},
	Mrreviewer = {Gerold Alsmeyer},
	Number = {1},
	Pages = {53--67},
	Title = {Poisson equation, moment inequalities and quick convergence for {M}arkov random walks},
	Volume = {87},
	Year = {2000}}

@article{fuhlai01,
	Author = {Fuh, Cheng-Der and Lai, Tze Leung},
	Coden = {AAPBBD},
	Date-Added = {2008-05-20 18:16:53 -0500},
	Date-Modified = {2008-05-20 18:16:53 -0500},
	Fjournal = {Advances in Applied Probability},
	Issn = {0001-8678},
	Journal = {Adv. in Appl. Probab.},
	Mrclass = {60K05 (60J10 60K15)},
	Mrnumber = {MR1860094 (2002f:60170)},
	Mrreviewer = {Gerold Alsmeyer},
	Number = {3},
	Pages = {652--673},
	Title = {Asymptotic expansions in multidimensional {M}arkov renewal theory and first passage times for {M}arkov random walks},
	Volume = {33},
	Year = {2001}}

@incollection{bor99a,
	Abstract = {The author considers a family of {Markov} processes on a Polish space $S$, each with a unique invariant probability measure. The family is called uniformly stable if the associated set of invariant probabilities is a compact set in the space of probability measures on $S$ endowed with the Prokhorov topology. For controlled countable {Markov} chains (MCs) and for controlled diffusions, the author proposes several equivalent conditions that ensure this set is compact, in particular: (a) a uniform integrability condition on some return time under stationary (or randomized stationary) policies for controlled MCs and under {Markov} policies for controlled diffusions, and (b) a stochastic {Lyapunov} condition.},
	Address = {Boston, MA},
	Author = {Borkar, Vivek S.},
	Booktitle = {System theory: modeling, analysis and control (Cambridge, MA, 1999)},
	Date-Added = {2008-05-20 11:53:03 -0500},
	Date-Modified = {2008-05-20 11:53:10 -0500},
	Mrclass = {93E15 (60J60 90C40 93E35)},
	Mrnumber = {MR1801486 (2001j:93107)},
	Mrreviewer = {Jean B. Lasserre},
	Pages = {107--120},
	Publisher = {Kluwer Acad. Publ.},
	Series = {Kluwer Internat. Ser. Engrg. Comput. Sci.},
	Title = {Uniform stability of controlled {M}arkov processes},
	Volume = {518},
	Year = {2000}}

@inproceedings{tie91,
	Address = {Fairfax Station, Va},
	Author = {Tierney, L.},
	Booktitle = {Computer Science and Statistics: 23rd Symposium on the Interface},
	Date-Added = {2008-05-19 16:00:50 -0500},
	Date-Modified = {2008-05-19 16:00:50 -0500},
	Editor = {E.M.Keramides},
	Pages = {563-570},
	Publisher = {Interface Foundation},
	Title = {Exploring posterior distributions using {Markov} chains},
	Year = {1991}}

@article{fen99a,
	Author = {Feng, J.},
	Date-Added = {2008-05-19 15:54:55 -0500},
	Date-Modified = {2008-05-19 15:54:55 -0500},
	Journal = SPA,
	Pages = {165-212},
	Title = {Martingale problems for large deviations of {Markov} processes},
	Volume = {81},
	Year = {1999}}

@article{mil61,
	Author = {Miller, H.D.},
	Date-Added = {2008-04-26 15:56:26 -0500},
	Date-Modified = {2008-04-26 15:56:26 -0500},
	Journal = ANNMS,
	Pages = {1260-1270},
	Title = {A convexivity property in the theory of random variables defined on a finite {M}arkov chain},
	Volume = {32},
	Year = {1961}}

@article{hub65,
	Author = {Huber, P. J.},
	Date-Added = {2008-04-26 13:46:58 -0500},
	Date-Modified = {2008-04-26 14:55:51 -0500},
	Journal = ANNMS,
	Pages = {1753-1758},
	Title = {A Robust Version of the Probability Ratio Test},
	Volume = 36,
	Year = 1965}

@book{hub81,
	Address = {New York},
	Author = {Huber, P. J.},
	Date-Added = {2008-04-26 13:46:58 -0500},
	Date-Modified = {2008-04-26 13:48:37 -0500},
	Key = {Hube81},
	Publisher = {Wiley},
	Title = {Robust Statistics},
	Year = {1981}}

@article{csimat03,
	Author = {Csisz{\'{a}}r, I. and Mat\'{u}\v{s}, F.},
	Date-Added = {2008-04-26 13:34:32 -0500},
	Date-Modified = {2008-04-26 13:39:23 -0500},
	Journal = TIT,
	Number = {6},
	Pages = {1474--1490},
	Title = {Information Projections Revisited},
	Volume = {49},
	Year = {2003}}

@article{yorbru02,
	Author = {Yor, M. and Bru, B.},
	Date-Added = {2008-04-22 08:29:48 -0500},
	Date-Modified = {2008-04-22 08:29:48 -0500},
	Journal = {Finance and Stochastics},
	Number = {1},
	Pages = {3-47},
	Title = {Comments on the life and mathematical legacy of {Wolfgang Doeblin}},
	Url = {http://ideas.repec.org/a/spr/finsto/v6y2002i1p3-47.html},
	Volume = {6},
	Year = 2002,
	Bdsk-Url-1 = {http://ideas.repec.org/a/spr/finsto/v6y2002i1p3-47.html}}

@book{DoeblinMovie,
	Author = {Handwerk, A. and Willems, H.},
	Date-Added = {2008-04-22 08:18:29 -0500},
	Date-Modified = {2008-04-22 08:52:46 -0500},
	Isbn = {978-3-540-71960-1},
	Publisher = {Springer},
	Series = {VideoMATH},
	Title = {Wolfgang Doeblin: A mathematician rediscovered},
	Year = {2007}}

@inproceedings{ordwei04a,
	Abstract = {Let {X/sub t/} be a stationary finite-alphabet {Markov} chain and {Z/sub t/} denote its noisy version when corrupted by a discrete memoryless channel. Let P(X/sub t//spl isin//spl middot/|Z/sub -/spl infin///sup t/) denote the conditional distribution of X/sub t/ given all past and present noisy observations, a simplex-valued random variable. We present a new approach to bounding the entropy rate of {Z/sub t/} by approximating the distribution of this random variable. This approximation is facilitated by the construction and study of a {Markov} process whose stationary distribution determines the distribution of P(X/sub t//spl isin//spl middot/|Z/sub -/spl infin///sup t/). To illustrate the efficacy of this approach, we specialize it and derive concrete bounds for the case of a binary {Markov} chain corrupted by a binary symmetric channel (BSC). These bounds are seen to capture the behavior of the entropy rate in various asymptotic regimes.},
	Author = {Ordentlich, E. and Weissman, T.},
	Booktitle = {In Proc. IEEE Information Theory Workshop, San Antonio, TX},
	Date-Added = {2008-04-20 16:09:13 -0500},
	Date-Modified = {2008-04-20 16:09:21 -0500},
	Month = {October 24-29},
	Pages = {117- 122},
	Title = {New bounds on the entropy rate of hidden {Markov} processes},
	Year = {2004}}

@inproceedings{holgolgly05,
	Abstract = {This paper explores connections between Information Theory, {Lyapunov} exponents for products of random matrices, and hidden {Markov} models. Specifically, we will show that entropies associated with finite-state channels are equivalent to {Lyapunov} exponents. We use this result to show that the traditional prediction filter for hidden {Markov} models is not an irreducible {Markov} chain in our problem framework. Hence, we do not have access to many well-known properties of irreducible continuous state space {Markov} chains (e.g. a unique and continuous stationary distribution). However, by exploiting the connection between entropy and {Lyapunov} exponents and applying proof techniques from the theory of random matrix products we can solve abroad class of problems related to capacity and hidden {Markov} models. Our results provide strong regularity results for the non-irreducible prediction filter as well as some novel theoretical tools to address problems in these areas.},
	Author = {Holliday, T. and Glynn, P. and Goldsmith, A.},
	Booktitle = {Proc.~of the 44th IEEE Conference on Decision and Control and 2005 European Control Conference. CDC-ECC '05},
	Comment = {Formulation of H(X) as a {Lyapunov} top exponent of a product of random matrices},
	Date-Added = {2008-04-20 15:56:03 -0500},
	Date-Modified = {2008-04-20 15:56:03 -0500},
	Keywords = {HMM},
	Pages = {1756--1763},
	Title = {Shannon Meets {Lyapunov}: Connections between Information Theory and Dynamical Systems},
	Url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1582414},
	Year = {2005},
	Bdsk-Url-1 = {http://ieeexplore.ieee.org/xpls/abs%5C_all.jsp?arnumber=1582414}}

@article{holgolgly06,
	Author = {Holliday, T. and Goldsmith, A. J. and Glynn, P. W.},
	Date-Added = {2008-04-20 15:50:13 -0500},
	Date-Modified = {2008-04-20 15:50:41 -0500},
	Journal = TIT,
	Number = {8},
	Pages = {3509-3532},
	Title = {Capacity of Finite State Channels Based on {Lyapunov} Exponents of Random Matrices},
	Url = {http://dblp.uni-trier.de/db/journals/tit/tit52.html#HollidayGG06},
	Volume = {52},
	Year = {2006},
	Bdsk-Url-1 = {http://dblp.uni-trier.de/db/journals/tit/tit52.html#HollidayGG06}}

@article{wei99,
	Author = {Weiss, Y.},
	Date-Added = {2008-04-13 16:38:58 -0500},
	Date-Modified = {2008-04-13 16:38:58 -0500},
	Journal = {Computer Vision, 1999. The Proceedings of the Seventh IEEE International Conference on},
	Keywords = {computer vision, eigenvalues and eigenfunctions, image segmentation, matrix algebraaffinity matrix, algorithm performance, automatic image grouping, automatic image segmentation, block matrices, computer vision, eigendecomposition algorithms, eigenvectors, real images, stability, synthetic images},
	Pages = {975-982 vol.2},
	Title = {Segmentation using eigenvectors: a unifying view},
	Volume = {2},
	Year = {1999}}

@article{schsmomul98,
	Author = {Sch{\"o}lkopf, B. and Smola, A. J. and M{\"u}ller, K.-R.},
	Date-Added = {2008-04-13 16:38:58 -0500},
	Date-Modified = {2008-04-13 16:38:58 -0500},
	Journal = {Neural Computation},
	Number = {5},
	Pages = {1299-1319},
	Title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem},
	Volume = {10},
	Year = {1998}}

@inproceedings{trowakduabarbar06,
	Author = {Tropp, J.A. and Wakin, M.B. and Duarte, M.F. and Baron, D. and Baraniuk, R.G.},
	Booktitle = {Proc.~of the {2006 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
	Date-Added = {2008-04-17 09:02:29 -0500},
	Date-Modified = {2008-08-24 13:10:23 -0500},
	Doi = {10.1109/ICASSP.2006.1660793},
	Issn = {1520-6149},
	Keywords = {signal reconstruction, signal sampling, smoothing methods, stochastic processes, wavelet transformsFIR filter, Poisson processes, compressed sensing, compressible signals, compressive sampling, nonlinear orthogonal matching pursuit algorithm, piecewise smooth signals, random acquisition techniques, random filtering, signal reconstruction, signals sparse, time-invariant structure, wavelet domains},
	Title = {Random Filters for Compressive Sampling and Reconstruction},
	Volume = {3},
	Year = {14-19 May 2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ICASSP.2006.1660793}}

@article{cantao06a,
	Author = {Cand{\`e}s, Emmanuel J. and Tao, Terence},
	Biburl = {http://www.bibsonomy.org/bibtex/27841d275ea6ecc49b6bcaaa466462160/dblp},
	Date = {2007-02-28},
	Date-Added = {2008-04-17 09:02:29 -0500},
	Date-Modified = {2008-04-17 09:02:29 -0500},
	Description = {dblp},
	Ee = {http://doi.ieeecomputersociety.org/10.1109/TIT.2006.885507},
	Journal = TIT,
	Keywords = {dblp},
	Number = {12},
	Pages = {5406-5425},
	Title = {Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?},
	Url = {http://dblp.uni-trier.de/db/journals/tit/tit52.html#CandesT06},
	Volume = {52},
	Year = {2006},
	Bdsk-Url-1 = {http://dblp.uni-trier.de/db/journals/tit/tit52.html#CandesT06}}

@book{bor08a,
	Address = {{Delhi, India and Cambridge, UK}},
	Author = {Borkar, V. S.},
	Date-Added = {2008-04-12 21:14:22 -0500},
	Date-Modified = {2008-12-09 15:07:27 -0600},
	Publisher = {{Hindustan Book Agency and Cambridge University Press (jointly)}},
	Title = {Stochastic Approximation: A Dynamical Systems Viewpoint},
	Year = {2008}}

@article{formeymoupri08a,
	Author = {Fort, G. and Meyn, S. P. and Moulines, E. and Priouret, P.},
	Date-Added = {2008-04-01 21:45:52 -0500},
	Date-Modified = {2008-04-01 21:45:52 -0500},
	Journal = ANNAP,
	Number = {2},
	Pages = {664-707},
	Title = {{ODE} methods for skip-free {Markov} chain stability with applications to {MCMC}},
	Volume = {18},
	Year = {2008}}

@article{tie94,
	Abstract = {		
This interesting paper is a survey of {Markov} chain Monte Carlo (MCMC) methods for computing characteristics of posterior distributions. In particular, it discusses the Gibbs sampler, the Metropolis algorithm and some hybrid strategies. Results from the theory of general state space {Markov} chains are used to derive properties of these algorithms and to suggest improvements for some of them. Practical issues that arise in the implementation of MCMC methods are also discussed. Thus, on the one hand, the paper provides a sound theoretical basis for the use of MCMC algorithms in Bayesian inference and, on the other hand, it also gives valuable practical guidance. The discussion section is as important and interesting as the paper itself. The subjects treated include convergence issues, central limit theorems, hybrid algorithms, and numerical stability, among others.},
	Author = {Tierney, Luke},
	Coden = {ASTSC7},
	Date-Added = {2008-03-27 06:46:00 -0500},
	Date-Modified = {2008-03-27 06:46:15 -0500},
	Fjournal = {The Annals of Statistics},
	Issn = {0090-5364},
	Journal = ANNS,
	Mrclass = {60J05 (62-04 62E25 62F15 65C05)},
	Mrnumber = {MR1329166 (96m:60150)},
	Mrreviewer = {On{\'e}simo Hern{\'a}ndez Lerma},
	Note = {With discussion and a rejoinder by the author},
	Number = {4},
	Pages = {1701--1762},
	Title = {Markov chains for exploring posterior distributions},
	Volume = {22},
	Year = {1994},
	Bdsk-File-1 = {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}}

@article{donvarIV,
	Author = {Donsker, M.D. and Varadhan, S.R.S.},
	Date-Added = {2008-03-04 16:40:21 -0600},
	Date-Modified = {2008-05-18 06:45:00 -0500},
	Journal = {Comm. Pure Appl. Math.},
	Number = {2},
	Pages = {183-212},
	Title = {Asymptotic evaluation of certain {M}arkov process expectations for large time. {I}{V}},
	Volume = {36},
	Year = {1983}}

@article{donvarIII,
	Author = {Donsker, M.D. and Varadhan, S.R.S.},
	Date-Added = {2008-03-04 16:40:21 -0600},
	Date-Modified = {2008-05-18 06:45:12 -0500},
	Journal = {Comm. Pure Appl. Math.},
	Number = {4},
	Pages = {389-461},
	Title = {Asymptotic evaluation of certain {M}arkov process expectations for large time. {I}{I}{I}},
	Volume = {29},
	Year = {1976}}

@article{donvarI-II,
	Author = {Donsker, M.D. and Varadhan, S.R.S.},
	Date-Added = {2008-03-04 16:40:21 -0600},
	Date-Modified = {2008-05-18 06:44:47 -0500},
	Journal = {Comm. Pure Appl. Math.},
	Pages = {1-47; ibid. {\bf 28} (1975), 279-301},
	Title = {Asymptotic evaluation of certain {M}arkov process expectations for large time. {I}. {I}{I}},
	Volume = {28},
	Year = {1975}}

@book{basnik93,
	Address = {Upper Saddle River, NJ, USA},
	Author = {Basseville, M. and Nikiforov, I. V.},
	Date-Added = {2008-02-25 08:19:00 -0600},
	Date-Modified = {2008-02-25 08:19:00 -0600},
	Isbn = {0-13-126780-9},
	Publisher = {Prentice-Hall, Inc.},
	Title = {Detection of abrupt changes: theory and application},
	Year = {1993}}

@article{laisha99,
	Abstract = {This paper addresses a number of open problems concerning the generalized likelihood ratio (GLR) rules for online detection of faults and parameter changes in control systems. It is shown that with an appropriate choice of the threshold and window size, these GLR rules are asymptotically optimal. The rules are also extended to non-likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing Gaussian approximations to these statistics when the window size is chosen suitably. Recursive algorithms are developed for practical implementation of the procedure, and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate},
	Author = {Lai, T. L. and Shan, J. Z.},
	Date-Added = {2008-02-25 08:17:44 -0600},
	Date-Modified = {2008-02-25 08:17:52 -0600},
	Journal = TAC,
	Number = {5},
	Pages = {952 - 966},
	Title = {Efficient recursive algorithms for detection of abrupt changes insignals and control systems},
	Volume = {44},
	Year = {1999}}

@unpublished{hansch08,
	Author = {Hansen, L. P. and Scheinkman, J.},
	Date-Added = {2008-02-18 12:44:50 -0800},
	Date-Modified = {2008-02-18 12:44:50 -0800},
	Note = {in preparation},
	Title = {Long Term Risk: An Operator Approach},
	Year = {2008}}

@article{bax04a,
	Author = {Baxendale, P.},
	Date-Added = {2008-02-13 11:45:57 -0600},
	Date-Modified = {2008-02-13 11:45:57 -0600},
	Journal = SPA,
	Pages = {235-272},
	Title = {Stochastic averaging and asymptotic behavior of the stochastic {Duffing-van der Pol} equation},
	Volume = {113},
	Year = {2004}}

@article{bhabor96a,
	Author = {Bhatt, A. G. and Borkar, V. S.},
	Date-Added = {2008-01-26 12:10:52 -0600},
	Date-Modified = {2008-01-26 12:10:52 -0600},
	Journal = ANNAP,
	Pages = {1531-1562},
	Title = {Occupation measures for controlled {Markov} processes: characterization and optimality},
	Volume = {24},
	Year = {1996},
	Bdsk-File-1 = {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}}

@techreport{barbor08,
	Author = {Barman, K. and Borkar, V. S.},
	Date-Added = {2008-01-20 15:12:41 -0500},
	Date-Modified = {2008-01-20 16:09:40 -0500},
	Institution = {Tata Institute for Fundamental Research},
	Title = {A note on linear function approximation using random projections},
	Year = {2008}}

@article{canromtao06,
	Author = {Cand{\`e}s, E. J. and Romberg, J. K. and Tao, T.},
	Date-Added = {2008-01-20 14:34:22 -0500},
	Date-Modified = {2008-01-20 14:34:53 -0500},
	Journal = TIT,
	Number = {2},
	Pages = {489-509},
	Title = {Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information},
	Volume = {52},
	Year = {2006}}

@article{don06a,
	Author = {Donoho, D. L.},
	Date-Added = {2008-01-20 14:34:22 -0500},
	Date-Modified = {2008-08-24 13:06:07 -0500},
	Journal = TIT,
	Number = {4},
	Pages = {1289--1306},
	Title = {Compressed Sensing},
	Volume = {52},
	Year = {2006},
	Bdsk-File-1 = {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}}

@inproceedings{zhagatbenmcc05,
	Author = {Zhang, D. and Gatica-Perez, D. and Bengio, S. and McCowan, I.},
	Booktitle = {Proceeedings of IEEE Conf. on Computer Vision and Pattern Rec. (CVPR),},
	Date-Added = {2008-01-20 14:23:14 -0500},
	Date-Modified = {2008-01-20 14:23:14 -0500},
	Month = {June},
	Pages = {68-71},
	Title = {Semi-supervised Adapted {HMMs} for Unusual Event Detection},
	Year = {2005}}

@article{tarvee04,
	Author = {Tartakovsky, A. G. and Veeravalli, V. V.},
	Date-Added = {2008-01-20 13:48:03 -0500},
	Date-Modified = {2008-01-20 13:48:57 -0500},
	Journal = {SIAM Theory of Probability and its Applications},
	Number = {3},
	Pages = {538-582},
	Title = {General Asymptotic {Bayesian} Theory of Quickest Change Detection},
	Volume = {49},
	Year = {2004}}

@unpublished{poltar07,
	Author = {Pollak, M. and Tartakovsky, A. G.},
	Date-Added = {2008-01-20 13:35:08 -0500},
	Date-Modified = {2008-01-20 14:15:04 -0500},
	Note = {Cite as: arXiv:math/0609780v2 [math.PR]},
	Title = {Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of {Markov} Processes with Applications to Quickest Change Detection},
	Year = 2007}

@article{lai01,
	Author = {Lai, T.L.},
	Date-Added = {2008-01-20 13:20:44 -0500},
	Date-Modified = {2008-01-20 13:21:30 -0500},
	Journal = {Stat. Sin.},
	Pages = {303-408},
	Title = {Sequential analysis: some classical problems and new challenges},
	Volume = {11},
	Year = {2001}}

@article{myktieyu95,
	Author = {Mykland, P. and Tierney, L. and Yu, B.},
	Date-Added = {2008-01-19 21:22:21 -0500},
	Date-Modified = {2008-01-19 21:22:21 -0500},
	Journal = JASA,
	Number = {429},
	Title = {Regeneration in {Markov} Chain Samplers},
	Volume = {90},
	Year = {1995}}

@incollection{mey91a,
	Address = {New York, NY, USA},
	Author = {Meyn, S. P.},
	Booktitle = {Topics in stochastic systems: modelling, estimation and adaptive control},
	Date-Added = {2008-01-19 21:02:40 -0500},
	Date-Modified = {2008-01-19 21:02:40 -0500},
	Editor = {Gerencs\'{e}r, L. and Caines, P. E.},
	Pages = {369-401},
	Publisher = {Springer-Verlag},
	Title = {Stability of {Markov} chains on topological spaces with applications to adaptive control and time series analysis},
	Year = {1991}}

@article{smirob94,
	Author = {Roberts, G.O. and Smith, A.F.M.},
	Date-Added = {2008-01-19 20:53:45 -0500},
	Date-Modified = {2008-01-19 20:53:45 -0500},
	Journal = SPA,
	Number = {2},
	Pages = {207--216},
	Title = {Simple conditions for the convergence of the {Gibbs} sampler and {Hastings-Metropolis} algorithms},
	Volume = {49},
	Year = {1994}}

@article{fle78a,
	Author = {Fleming, W.H.},
	Date-Added = {2008-01-19 18:55:01 -0500},
	Date-Modified = {2008-01-19 18:55:01 -0500},
	Journal = {App. Math. Optim.},
	Pages = {329-346},
	Title = {Exit probabilities and optimal stochastic control},
	Volume = {4},
	Year = 1978}

@book{fenkur06a,
	Address = {Providence, U.S.A.},
	Author = {Feng, J. and Kurtz, T. G.},
	Date-Added = {2008-01-19 18:46:56 -0500},
	Date-Modified = {2008-01-19 18:46:56 -0500},
	Isbn = {0-8218-4145-9},
	Publisher = {American Mathematical Society},
	Series = {Mathematical Surveys and Monographs},
	Title = {Large Deviations for Stochastic Processes},
	Volume = {131},
	Year = {2006}}

@article{kipvar86,
	Abstract = {Let $\{X_n\}_{n\ge0}$ be a stationary, reversible, ergodic {Markov} chain on some state space $S$, with $X_0$ distributed according to the invariant distribution $\pi(ds)$. Let $V$ be a function on $S$ such that $E\{V(X_0)\}=\int V(s)\pi(ds)=0$, $E\{V^2(X_0)\}<\infty$ and such that $\sigma^2=\sum^{+\infty} _{-\infty}E\{V(X_0)V(X_n)\}$ converges. The authors prove that, under these weak conditions, $Y_n(t):=n^{-1/2}\sum^{[nt]}_1 V(X_n)$ converges weakly to a Brownian motion $\sigma B(t)$ with variance $\sigma^2$.},
	Author = {Kipnis, C. and Varadhan, S. R. S.},
	Coden = {CMPHAY},
	Date-Added = {2008-01-18 12:38:59 -0600},
	Date-Modified = {2008-01-18 12:39:03 -0600},
	Fjournal = {Communications in Mathematical Physics},
	Issn = {0010-3616},
	Journal = {Comm. Math. Phys.},
	Mrclass = {60F17 (60J05 60K35)},
	Mrnumber = {MR834478 (87i:60038)},
	Mrreviewer = {H. Kesten},
	Number = {1},
	Pages = {1--19},
	Title = {Central limit theorem for additive functionals of reversible {M}arkov processes and applications to simple exclusions},
	Volume = {104},
	Year = {1986}}

@article{mehhagban05,
	Author = {Mehta, P. G. and Hagen, G. and Banaszuk, A.},
	Date-Added = {2008-01-08 19:23:00 -0600},
	Date-Modified = {2008-01-08 19:23:16 -0600},
	Journal = {SIAM Dynamical Systems Magazine (DS Web)},
	Title = {Dynamical Systems in Jet Engines: A Symmetry Based Approach},
	Url = {http://www.dynamicalsystems.org/ma/ma/display?item=128},
	Year = {October, 2005},
	Bdsk-Url-1 = {http://www.dynamicalsystems.org/ma/ma/display?item=128}}

@article{huisch05a,
	Author = {Huisinga, W. and Schmidt, B.},
	Date-Added = {2008-01-08 18:10:41 -0600},
	Date-Modified = {2008-01-08 18:10:41 -0600},
	Journal = {In 'Advances in Algorithms for Macromolecular Simulation', Lecture Notes in Computational Science and Engineering, Springer},
	Title = {Metastability and Dominant Eigenvalues of Transfer Operators},
	Year = {2005}}

@article{chohalkup00,
	Author = {Chorin, A. and Hald, O. and Kupferman, R.},
	Date-Added = {2008-01-03 19:30:05 -0600},
	Date-Modified = {2008-01-03 19:30:05 -0600},
	Journal = {Proc. Nat. Acad. Sci.},
	Pages = {2968-2973},
	Title = {Optimal prediction and the {Mori-Zwanzig} representation of irreversible processes},
	Volume = {97},
	Year = {2000}}

@article{phikok81,
	Author = {Phillips, R. G. and Kokotovic, P. V.},
	Date-Added = {2008-01-02 19:15:30 -0600},
	Date-Modified = {2008-01-02 19:15:30 -0600},
	Journal = TAC,
	Number = {5},
	Title = {A Singular Pertubation Approach to Modeling and Control of {M}arkov Chains},
	Volume = {26},
	Year = {1981}}

@article{robros99a,
	Author = {Roberts, G. O. and Rosenthal, J. S.},
	Date-Added = {2007-12-31 17:43:56 -0600},
	Date-Modified = {2007-12-31 17:43:56 -0600},
	Journal = JRSSB,
	Pages = {643--660},
	Title = {Convergence of the slice sampler},
	Volume = {61},
	Year = {1999}}

@article{fulwil99,
	Author = {Fulman, J. and Wilmer, E. L.},
	Date-Added = {2007-12-31 17:18:33 -0600},
	Date-Modified = {2007-12-31 17:18:33 -0600},
	Journal = ANNAP,
	Number = {1},
	Pages = {1-13},
	Title = {Comparing eigenvalue bounds for {Markov} chains: when does {Poincar\'e} beat {Cheeger}?},
	Volume = {9},
	Year = {1999}}

@article{diasal96,
	Abstract = {This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of {Markov} chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous time. Some aspects of the theory simplify considerably with finite state spaces and we are able to give a self-contained development. Examples of applications include the study of a Metropolis chain for the binomial distribution, sharp results for natural chains on the box of side n in d dimensions and improved rates for exclusion processes. We also show that for most r-regular graphs the log-Sobolev constant is of smaller order than the spectral gap. The log-Sobolev constant of the asymmetric two-point space is computed exactly as well as the log-Sobolev constant of the complete graph on n points.
},
	Author = {Diaconis, P. and Saloff-Coste, L.},
	Date-Added = {2007-12-31 17:13:37 -0600},
	Date-Modified = {2007-12-31 17:13:48 -0600},
	Journal = ANNAP,
	Number = {3},
	Pages = {695-750},
	Title = {Logarithmic Sobolev inequalities for finite {Markov} chains},
	Volume = {6},
	Year = {1996}}

@misc{catguiwanwu08,
	Abstract = {We show how to use {Lyapunov} functions to obtain functional inequalities which are stronger than Poincar{\'e} inequality (for instance logarithmic Sobolev or F-Sobolev). The case of Poincar{\'e} and weak Poincar{\'e} inequalities was studied in Bakry and al. This approach allows us to recover and extend in an unified way some known criteria in the euclidean case (Bakry-Emery, Wang, Kusuoka-Stroock ...). },
	Author = {Cattiaux, P. and Guillin, A. and Wang, F.-Y. and Wu, L.},
	Date-Added = {2007-12-31 17:08:04 -0600},
	Date-Modified = {2008-05-19 16:00:04 -0500},
	Howpublished = {Available on Math. ArXiv 0712.0235},
	Title = {{Lyapunov} conditions for logarithmic {Sobolev} and Super {Poincar\'e} inequality},
	Url = {http://www.citebase.org/abstract?id=oai:arXiv.org:0712.0235},
	Year = {2007},
	Bdsk-Url-1 = {http://www.citebase.org/abstract?id=oai:arXiv.org:0712.0235}}

@book{nor97,
	Address = {Cambridge},
	Author = {Norris, J.R.},
	Date-Added = {2007-12-31 17:00:04 -0600},
	Date-Modified = {2007-12-31 17:00:16 -0600},
	Publisher = {Cambridge University Press},
	Series = {Cambridge Series in Statistical and Probabilistic Mathematics},
	Title = {Markov Chains},
	Year = {1997}}

@article{jarrob02,
	Author = {Jarner, S. F. and Roberts, G. O.},
	Date-Added = {2007-12-31 15:15:16 -0600},
	Date-Modified = {2007-12-31 15:15:16 -0600},
	Journal = ANNAP,
	Number = {1},
	Pages = {224-247},
	Title = {Polynomial Convergence Rates of {Markov} Chains},
	Volume = {12},
	Year = {2002}}

@article{ormsen02,
	Address = {Hingham, MA, USA},
	Author = {Ormoneit, Dirk and Sen, \'{S}aunak},
	Date-Added = {2007-12-28 14:36:44 -0600},
	Date-Modified = {2007-12-28 14:36:44 -0600},
	Issn = {0885-6125},
	Journal = {Mach. Learn.},
	Number = {2-3},
	Pages = {161--178},
	Publisher = {Kluwer Academic Publishers},
	Title = {Kernel-Based Reinforcement Learning},
	Volume = {49},
	Year = {2002}}

@article{tsivan96,
	Author = {Tsitsiklis, J. N. and Van Roy, B.},
	Date-Added = {2007-12-13 11:15:03 -0600},
	Date-Modified = {2008-12-21 09:17:26 -0600},
	Issn = {0885-6125},
	Journal = {Mach. Learn.},
	Number = {1-3},
	Pages = {59--94},
	Title = {Feature-based methods for large scale dynamic programming},
	Volume = {22},
	Year = {1996}}

@article{fil91,
	Author = {Fill, J. A.},
	Date-Added = {2007-12-13 10:32:54 -0600},
	Date-Modified = {2007-12-13 10:35:17 -0600},
	Journal = ANNAP,
	Number = {1},
	Pages = {62-87},
	Title = {Eigenvalue Bounds on Convergence to Stationarity for Nonreversible {Markov} Chains, with an Application to the Exclusion Process},
	Volume = {1},
	Year = {1991}}

@article{robros04,
	Abstract = {This is a survey paper on {Markov} chains on general state spaces. The authors start with an introduction to {Markov} chain Monte Carlo (MCMC) algorithms such as the Metropolis-Hastings algorithm and the Gibbs sampler. Examples of some applications to Bayesian statistics are also presented.

After this introductory material, the authors discuss some theoretical questions that arise in the context of MCMC algorithms such as the rate of convergence to stationarity, and present some sufficient conditions for geometric and uniform ergodicity of a {Markov} chain. In the next section, using coupling arguments, most of these results are proved.

Furthermore, MCMC central limit theorems, optimal scaling problems and weak convergence results are also presented.

It should be said that although there are no new results about {Markov} chains in this paper, many of the proofs are essentially new.
Reviewed by Roman Urban
},
	Author = {Roberts, G. O. and Rosenthal, J. S.},
	Date-Added = {2007-12-04 09:18:00 -0600},
	Date-Modified = {2007-12-31 17:43:52 -0600},
	Fjournal = {Probability Surveys},
	Issn = {1549-5787},
	Journal = {Probab. Surv.},
	Mrclass = {60J05 (62F10 65C05)},
	Mrnumber = {MR2095565 (2005i:60135)},
	Mrreviewer = {Roman Urban},
	Pages = {20--71 (electronic)},
	Title = {General state space {M}arkov chains and {MCMC} algorithms},
	Volume = {1},
	Year = {2004}}

@article{kocree06,
	Abstract = {According to a 1975 result of T. Kaijser, if some nonvanishing product of
hidden {Markov} model (HMM) stepping matrices is subrectangular, and the
underlying chain is aperiodic, the corresponding $\alpha$-chain has a unique
invariant limiting measure $\lambda$. Here the $\alpha$-chain
$\{\alpha_n\}=\{(\alpha_{ni})\}$ is given by \[\alpha_{ni}=P(X_n=i|
Y_n,Y_{n-1},...),\] where $\{(X_n,Y_n)\}$ is a finite state HMM with unobserved
Markov chain component $\{X_n\}$ and observed output component $\{Y_n\}$. This
defines $\{\alpha_n\}$ as a stochastic process taking values in the probability
simplex. It is not hard to see that $\{\alpha_n\}$ is itself a {Markov} chain.
The stepping matrices $M(y)=(M(y)_{ij})$ give the probability that
$(X_n,Y_n)=(j,y)$, conditional on $X_{n-1}=i$. A matrix is said to be
subrectangular if the locations of its nonzero entries forms a cartesian
product of a set of row indices and a set of column indices. Kaijser's result
is based on an application of the Furstenberg--Kesten theory to the random
matrix products $M(Y_1)M(Y_2)... M(Y_n)$. In this paper we prove a slightly
stronger form of Kaijser's theorem with a simpler argument, exploiting the
theory of e chains.  
},
	Author = {Kochman, F. and Reeds, J.},
	Date-Added = {2007-12-04 05:39:35 -0600},
	Date-Modified = {2007-12-04 05:41:51 -0600},
	Fjournal = {The Annals of Applied Probability},
	Issn = {1050-5164},
	Journal = ANNAP,
	Mrclass = {60J10 (60F99 60J05)},
	Mrnumber = {MR2288705},
	Number = {4},
	Pages = {1805--1815},
	Title = {A simple proof of {K}aijser's unique ergodicity result for hidden {M}arkov {$\alpha$}-chains.},
	Volume = {16},
	Year = {2006}}

@article{atazei97,
	Abstract = {Consider the Wonham optimal filtering problem for a finite state ergodic {Markov} process in both discrete and continuous time, and let $\sigma$ be the noise intensity for the observation. We examine the sensitivity of the solution with respect to the filter's initial conditions in terms of the gap between the first two {Lyapunov} exponents of the Zakai equation for the unnormalized conditional probability. This gap is studied in the limit as $\sigma\to 0$ by techniques involving considerations of nonlinear filtering and the stochastic Feynman-Kac formula. Conditions are given for the limit to be either negative or $-\infty$. Asymptotic bounds are derived in the latter case.},
	Author = {Atar, R. and Zeitouni, O.},
	Coden = {SJCODE},
	Date-Added = {2007-12-04 05:37:23 -0600},
	Date-Modified = {2007-12-04 05:38:34 -0600},
	Fjournal = {SIAM Journal on Control and Optimization},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {93E11 (60J57)},
	Mrnumber = {MR1430282 (97k:93065)},
	Mrreviewer = {Sergei A. Avdonin},
	Number = {1},
	Pages = {36--55},
	Title = {{Lyapunov} exponents for finite state nonlinear filtering},
	Volume = {35},
	Year = {1997}}

@article{luntwe96a,
	Author = {Lund, R. and Tweedie, R. L.},
	Date-Added = {2007-11-30 23:39:06 -0600},
	Date-Modified = {2007-11-30 23:39:06 -0600},
	Journal = MOR,
	Pages = {182--194},
	Title = {Geometric convergence rates for stochastically ordered {Markov} chains},
	Volume = {20},
	Year = {1996}}

@article{robtwe96a,
	Author = {Roberts, G. O. and Tweedie, R. L.},
	Date-Added = {2007-11-30 23:18:00 -0600},
	Date-Modified = {2007-11-30 23:18:28 -0600},
	Journal = {Biometrika},
	Pages = {95--100},
	Title = {Geometric convergence and {Central Limit Theorems} for multidimensional {Hastings and Metropolis} algorithms},
	Volume = {83},
	Year = {1996}}

@article{mentwe96a,
	Author = {Mengersen, K.L. and Tweedie, R.L.},
	Date-Added = {2007-11-30 23:12:56 -0600},
	Date-Modified = {2007-12-31 17:23:45 -0600},
	Journal = ANNS,
	Pages = {101--121},
	Title = {Rates of convergence of the {Hastings and Metropolis} algorithms},
	Volume = {24},
	Year = {1996}}

@inproceedings{melrib07,
	Author = {Melo, Francisco S. and Ribeiro, M. Isabel},
	Booktitle = {Proceedings of the {2007 European Control Conference}},
	Date-Added = {2007-11-18 22:48:07 -0600},
	Date-Modified = {2007-11-18 22:48:07 -0600},
	Pages = {2671-2678},
	Title = {Convergence of {Q-learning} with linear function approximation},
	Year = {2007}}

@article{bor03b,
	Author = {Borkar, V. S.},
	Date-Added = {2007-11-18 17:43:29 -0600},
	Date-Modified = {2007-11-18 17:43:29 -0600},
	Journal = SCL,
	Pages = {1-9},
	Title = {Avoidance of traps in stochastic approximation},
	Volume = {50},
	Year = {2003}}

@book{bor03a,
	Address = {Berlin},
	Author = {Borrelli, F.},
	Date-Added = {2007-11-18 17:43:29 -0600},
	Date-Modified = {2007-11-18 17:43:29 -0600},
	Pages = {xviii+206},
	Publisher = {Springer-Verlag},
	Series = {Lecture Notes in Control and Information Sciences},
	Title = {Constrained optimal control of linear and hybrid systems},
	Volume = {290},
	Year = {2003}}

@article{bor03c,
	Author = {Borkar, V. S.},
	Coden = {STOPB7},
	Date-Added = {2007-11-18 17:39:59 -0600},
	Date-Modified = {2007-11-18 17:43:11 -0600},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = SPA,
	Mrclass = {93E20 (60J05 90C39)},
	Mrnumber = {MR1950768 (2003m:93097)},
	Mrreviewer = {Bo{\.z}enna Pasik-Duncan},
	Number = {2},
	Pages = {293--310},
	Title = {Dynamic programming for ergodic control with partial observations},
	Volume = {103},
	Year = {2003}}

@article{bor00a,
	Author = {Borkar, V. S.},
	Date-Added = {2007-11-18 17:39:28 -0600},
	Date-Modified = {2007-11-18 17:39:28 -0600},
	Fjournal = {SIAM Journal on Control and Optimization},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {93E20 (90C40 93E11)},
	Mrnumber = {MR1786324 (2001i:93130)},
	Mrreviewer = {{\L}. Stettner},
	Number = {3},
	Pages = {673--681 (electronic)},
	Title = {Average cost dynamic programming equations for controlled {M}arkov chains with partial observations},
	Volume = {39},
	Year = {2000}}

@book{elllakmoo95,
	Address = {New York},
	Author = {Elliott, R. J. and Aggoun, L. and Moore, J. B.},
	Date-Added = {2007-11-18 17:38:29 -0600},
	Date-Modified = {2007-11-18 17:38:29 -0600},
	Isbn = {0-387-94364-1},
	Mrclass = {93-02 (60J10 62M05 93E03 94A12)},
	Mrnumber = {MR1323178 (96h:93001)},
	Mrreviewer = {Bo{\.z}enna Pasik-Duncan},
	Note = {Estimation and control},
	Pages = {xii+361},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Hidden {M}arkov models},
	Volume = {29},
	Year = {1995}}

@book{sutbar98,
	Address = {Cambridge, MA},
	Author = {Sutton, R.S. and Barto, A.G.},
	Date-Added = {2007-11-18 15:49:11 -0600},
	Date-Modified = {2008-12-29 08:00:19 -0600},
	Edition = {On-line edition at http://www.cs.ualberta.ca/\~{ }sutton/book/the-book.html},
	Publisher = {{MIT Press}},
	Title = {Reinforcement Learning: An Introduction},
	Year = {1998}}

@unpublished{guileowuyao07,
	Author = {Guillin, A. and Leonard, C. and Wu, L. and Yao, N.},
	Date-Added = {2007-11-09 18:37:16 -0600},
	Date-Modified = {2007-11-09 18:37:28 -0600},
	Note = {unpublished ms. Preprint available at http://www.latp.univ-mrs.fr/\~{ }guillin/index3.html},
	Title = {Transportation inequalities for {Markov} processes},
	Year = {2007}}

@article{gonwu06a,
	Author = {Gong, F.Z. and Wu, L.M.},
	Date-Added = {2007-11-09 18:24:09 -0600},
	Date-Modified = {2007-11-09 18:24:09 -0600},
	Journal = {J. Math. Pures Appl.},
	Pages = {151-191},
	Title = {Spectral gap of positive operators and applications},
	Volume = {85},
	Year = {2006},
	Bdsk-File-1 = {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}}

@article{wu95a,
	Author = {Wu, L.M.},
	Date-Added = {2007-11-09 18:13:18 -0600},
	Date-Modified = {2007-11-09 18:13:18 -0600},
	Journal = {C. R. Acad. Sci Paris S\'erie I},
	Pages = {777--782},
	Title = {Large deviations for {Markov processes} under superboundedness},
	Volume = {324},
	Year = {1995}}

@article{avrlas99a,
	Abstract = {We consider a singularly perturbed (finite state) {Markov} chain and provide a complete characterization of the fundamental matrix. In particular, we obtain a formula for the regular part simpler than a previous formula obtained by Schweitzer, and the singular part is obtained via a reduction process similar to Delebecque's reduction for the stationary distribution. In contrast to previous approaches, one works with aggregate {Markov} chains of much smaller dimension than the original chain, an essential feature for practical computation. An application to mean first-passage times is also presented.

},
	Author = {Avrachenkov, K. E. and Lasserre, J. B.},
	Date-Added = {2007-11-03 10:46:29 -0500},
	Date-Modified = {2008-01-02 19:12:39 -0600},
	Journal = AAP,
	Number = {3},
	Pages = {679--697},
	Title = {The fundamental matrix of singularly perturbed {Markov} chains},
	Volume = {31},
	Year = {1999}}

@article{corvap95,
	Address = {Hingham, MA, USA},
	Author = {Cortes, C. and Vapnik, V.},
	Date-Added = {2007-10-22 19:59:07 -0500},
	Date-Modified = {2007-10-22 20:22:40 -0500},
	Doi = {http://dx.doi.org/10.1023/A:1022627411411},
	Issn = {0885-6125},
	Journal = ML,
	Number = {3},
	Pages = {273--297},
	Publisher = {Kluwer Academic Publishers},
	Title = {Support-Vector Networks},
	Volume = {20},
	Year = {1995},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1022627411411}}

@inproceedings{formeymoupri06a,
	Address = {New York, NY, USA},
	Author = {Fort, G. and Moulines, E. and Meyn, S. P. and Priouret, P.},
	Booktitle = {{Valuetools} '06: Proceedings of the 1st international conference on Performance evaluation methodolgies and tools},
	Date-Added = {2007-10-04 09:45:46 -0500},
	Date-Modified = {2007-10-09 06:44:53 -0700},
	Doi = {http://doi.acm.org/10.1145/1190095.1190149},
	Isbn = {1-59593-504-5},
	Location = {Pisa, Italy},
	Pages = {42},
	Publisher = {ACM Press},
	Title = {{ODE} methods for {Markov} chain stability with applications to {MCMC}},
	Year = {2006},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/1190095.1190149}}

@article{fuh04,
	Abstract = {From the summary: "Let $\xi_0,\xi_1,\dots,\xi_{\omega-1} $ be observations from a hidden {Markov} model with probability distribution $ P^{\theta_0} $, and let $\xi_{\omega},\xi_{\omega+1},\dots$ be observations from the hidden {Markov} model with probability distribution $P^{\theta_1}$. The parameters ${\theta_0}$ and ${\theta_1}$ are given, while the change point $\omega$ is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from $P^{\theta_0}$ to $P^{\theta_1}$, but to avoid false alarms.

"In this paper we investigate the performance of the Shiryaev-Roberts-Pollak (SRP) rule for change point detection in the dynamic system of hidden {Markov} models. By making use of the {Markov} chain representation for the likelihood function, the structure of the asymptotically minimax policy of the Bayes rule, and sequential hypothesis testing theory for {Markov} random walks, we show that the SRP procedure is asymptotically minimax in the sense of M. Pollak \ref[Ann. Statist. 13 (1985), no. 1, 206--227; MR0773162 (86f:62137)]. Next, we present a second order asymptotic approximation for the expected stopping time when $\omega=1$. A nonlinear renewal theory for {Markov} random walks is also given."},
	Author = {Fuh, Cheng-Der},
	Coden = {ASTSC7},
	Date-Added = {2007-08-12 17:21:19 -0500},
	Date-Modified = {2007-12-04 09:15:16 -0600},
	Fjournal = {The Annals of Statistics},
	Issn = {0090-5364},
	Journal = ANNS,
	Keywords = {Change point detection, HMM},
	Mrclass = {60G40 (60F05 60J05 60J10 60K05 60K15)},
	Mrnumber = {MR2102511 (2005h:60123)},
	Mrreviewer = {Fabio P. Machado},
	Number = {5},
	Pages = {2305--2339},
	Title = {Asymptotic operating characteristics of an optimal change point detection in hidden {M}arkov models},
	Volume = {32},
	Year = {2004},
	Bdsk-File-1 = {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}}

@article{vee99,
	Author = {Veeravalli, V. V.},
	Date-Added = {2007-08-08 13:34:04 -0500},
	Date-Modified = {2007-08-08 13:34:04 -0500},
	Journal = {J. of The Franklin Institute},
	Month = {March},
	Number = {2},
	Pages = {301-322},
	Title = {Sequential Decision Fusion: {T}heory and Applications},
	Volume = {336},
	Year = 1999}

@book{neu81,
	Address = {New York},
	Author = {Neuts, Marcel F.},
	Date-Added = {2007-07-22 07:56:38 -0500},
	Date-Modified = {2007-07-22 07:56:38 -0500},
	Isbn = {0-486-68342-7},
	Mrclass = {60K25 (60-04 60J10)},
	Mrnumber = {MR1313503 (95k:60241)},
	Note = {Corrected reprint of the 1981 original},
	Pages = {xiv+332},
	Publisher = {Dover Publications Inc.},
	Title = {Matrix-geometric solutions in stochastic models. An algorithmic approach},
	Year = {1994}}

@incollection{herlas02a,
	Address = {Boston, MA},
	Author = {Hern{\'a}ndez-Lerma, On{\'e}simo and Lasserre, Jean B.},
	Booktitle = {Handbook of {Markov} decision processes},
	Date-Added = {2007-07-22 07:53:46 -0500},
	Date-Modified = {2007-07-22 07:53:46 -0500},
	Mrclass = {90C40 (90C05)},
	Mrnumber = {MR1887209},
	Pages = {377--407},
	Publisher = {Kluwer Acad. Publ.},
	Series = {Internat. Ser. Oper. Res. Management Sci.},
	Title = {The linear programming approach},
	Volume = {40},
	Year = {2002}}

@incollection{haukve03a,
	Address = {Cambridge, MA},
	Author = {Hauskrecht, M. and Kveton, B.},
	Booktitle = {Advances in Neural Information Processing Systems},
	Date-Added = {2007-07-22 07:50:00 -0500},
	Date-Modified = {2007-07-22 07:50:00 -0500},
	Journal = {Advances in Neural Information Processing Systems},
	Pages = {895-902},
	Publisher = {MIT Press},
	Title = {Linear program approximations to factored continuous-state {Markov} decision processes},
	Volume = {16},
	Year = {2004}}

@article{dekhor88a,
	Address = {Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA},
	Author = {Dekker, R. and Hordijk, A.},
	Date-Added = {2007-07-19 11:54:38 -0500},
	Date-Modified = {2007-07-19 11:54:38 -0500},
	Issn = {0364-765X},
	Journal = MOR,
	Number = {3},
	Pages = {395--420},
	Publisher = {INFORMS},
	Title = {Average, sensitive and Blackwell optimal policies in denumerable {Markov} decisionchains with unbounded rewards},
	Volume = {13},
	Year = {1988}}

@unpublished{matmeypassmi07a,
	Author = {Mathews, G. and Meyn, S. P. and Passini, J.-M. and Smith, T.},
	Date-Added = {2007-07-18 11:02:08 -0500},
	Date-Modified = {2007-07-18 11:02:08 -0500},
	Note = {In preparation},
	Title = {Learning macroscopic dynamics},
	Year = {2007}}

@article{zeemeimai98,
	Annote = {Summary: "We examine some mathematical aspects of learning unknown mappings with the mixture of experts model (MEM). Specifically, we observe that the MEM is at least as powerful as a class of neural networks, in a sense that we make precise. Upper bounds on the approximation error are established for a wide class of target functions. The general theorem states that\break $\|f-f_n\|_p\le c/n^{r/d}$ for $f\in W_p^r(L)$ (a Sobolev class over $[-1,1]^d)$, and $f_n$ belongs to an $n$-dimensional manifold of normalized ridge functions. The same bound holds for the MEM as a special case of the above. The stochastic error, in the context of learning from independent and identically distributed (i.i.d.) examples, is also examined. An asymptotic analysis establishes the limiting behavior of this error, in terms of certain pseudo-information matrices. These results substantiate the intuition behind the MEM, and motivate applications."},
	Author = {Zeevi, A. J. and Meir, R. and Maiorov, V.},
	Coden = {IETTAW},
	Date-Added = {2007-07-18 11:01:40 -0500},
	Date-Modified = {2007-07-18 11:01:54 -0500},
	Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory},
	Issn = {0018-9448},
	Journal = TIT,
	Mrclass = {68T05 (62F99 92B20)},
	Mrnumber = {MR1616675 (99b:68160)},
	Number = {3},
	Pages = {1010--1025},
	Title = {Error bounds for functional approximation and estimation using mixtures of experts},
	Volume = {44},
	Year = {1998}}

@book{bis95a,
	Address = {New York},
	Annote = {
By concentrating on pattern recognition aspects of neural networks, the author is able to treat many important topics in much greater depth. The most important contribution of the book is the solid statistical pattern recognition approach, a sign of increasing maturity of the field.
},
	Author = {Bishop, C. M.},
	Date-Added = {2007-07-18 11:00:45 -0500},
	Date-Modified = {2007-07-18 11:01:19 -0500},
	Isbn = {0-19-853849-9; 0-19-853864-2},
	Mrclass = {68T10 (92B20)},
	Mrnumber = {MR1385195 (97m:68172)},
	Mrreviewer = {R{\u{a}}zvan Andonie},
	Note = {With a foreword by Geoffrey Hinton},
	Pages = {xviii+482},
	Publisher = {The Clarendon Press Oxford University Press},
	Title = {Neural networks for pattern recognition},
	Year = {1995}}

@article{lip745,
	Annote = {Semi-Markov decision processes with unbounded rewards are studied. The author gives the conditions for the existences of $\varepsilon$-optimal and optimal stationary policies in the case when the state space is countable or general. He also gives the relation between an optimality equation and an optimal policy. Queueing problems are mentioned as an application.

\{Reviewer's remark: The author does not impose any condition on the manner in which the set $A_x$ of actions feasible at state $x$ depends on $x$. This fact, in the case of general state space, leads to a crucial fault on the measurability of the optimal return over $n$-stages, and consequently it does the same over the infinite future. The author claims that if each $A_x$ is countable and if $\gamma(x,a)$ is Borel measurable in $(x,a)$, then $u(x)=\sup_{a\in A_x}\gamma(x,a)$ is Borel measurable. The reviewer, however, has a simple counterexample as follows. Consider the case when $\gamma$ is independent of $x$ and is given by $\gamma(x,a)=a$ for $a,x\inR^1$. Choose two real numbers $a_1$ and $a_2$ so that $a_1\neq a_2$, choose a non-Borel subset $S_1$ of $R^1$, and put $S_2=S_1{}^c$. Suppose that $A_x=\{a_1\}$ or $\{a_2\}$ depending on whether $x\in S_1$ or $S_2$. Then we have $u(x)=a_1$ or $a_2$ depending on whether $x\in S_1$ or $S_2$, which is not a Borel measurable function.\}
Reviewed by Nagata Furukawa},
	Author = {Lippman, Steven A.},
	Date-Added = {2007-07-15 12:27:16 -0500},
	Date-Modified = {2007-07-15 12:27:40 -0500},
	Fjournal = {Management Science. Journal of the Institute of Management Science. Application and Theory Series},
	Issn = {0025-1909},
	Journal = MS,
	Keywords = {MDP},
	Mrclass = {90C45},
	Mrnumber = {MR0398535 (53 \#2386)},
	Mrreviewer = {Nagata Furukawa},
	Number = {11},
	Pages = {1225--1233},
	Title = {On dynamic programming with unbounded rewards},
	Volume = {21},
	Year = {1974/75}}

@article{vanwes77,
	Annote = {From the text: "S. A. Lippman [same journal 21 (1974/75), no. 11, 1225--1233; MR0398535 (53 \#2386)] considered a discounted semi-Markov decision process with general state space $S$ and action space $A$. Generalizing his approach of an earlier paper [ibid. 19 (1972/73), 717--731; MR0337340 (49 \#2109)], he presented sufficient conditions for the existence of a normed Banach space of real-valued functions on $S$ in which E. V. Denardo's $N$-stage contraction approach [SIAM Rev. 9 (1967), 165--177; MR0215608 (35 \#6448)] may be used. This approach allows the rewards of the {Markov} decision process to be unbounded to a certain extent. This is made possible by the specific choice of the norm in the Banach space. Lippman used weighted supremum norms which were later studied more generally for {Markov} decision processes by the second author [J. Math. Anal. Appl. 58 (1977), no. 2, 326--335; MR0441363 (55 \#14226)]. Another method of handling certain types of unbounded rewards has been introduced by J. M. Harrison [Ann. Math. Statist. 43 (1972), 636--644; MR0354023 (50 \#6505)]. His idea of a shifted space has been combined with the weighted supremum norm approach by the first author [ Contracting {Markov} decision processes, Math. Centrum, Amsterdam, 1976; MR0503842 (58 \#20474)]. In this note it is shown that these conditions may be replaced by somewhat weaker and simpler conditions."},
	Author = {van Nunen, J. A. E. E. and Wessels, J.},
	Coden = {MSCIAM},
	Date-Added = {2007-07-15 12:26:25 -0500},
	Date-Modified = {2007-07-15 12:26:41 -0500},
	Fjournal = {Management Science. Journal of the Institute of Management Science. Application and Theory Series},
	Issn = {0025-1909},
	Journal = MS,
	Keywords = {MDP},
	Mrclass = {90C40 (90C39)},
	Mrnumber = {MR521666 (81i:90202)},
	Number = {5},
	Pages = {576--580},
	Title = {A note on dynamic programming with unbounded rewards},
	Volume = {24},
	Year = {1977/78}}

@article{wij77,
	Annote = {credits He and Wessels for weighted V norm

Author's summary: "In this paper stationary {Markov} decision problems are considered with an arbitrary state space and a compact space of strategies. Conditions are given for the existence of an average optimal strategy. This is done by using the fact that a continuous function on a compact space attains its minimum. To prove the continuity of the average cost as a function on the space of strategies some perturbation results for quasicompact linear operators are used. In a first set of conditions, the boundedness of the one-period cost functions and the quasicompactness of the {Markov} processes are assumed. In more general conditions the boundedness of the cost functions is replaced by the boundedness, on a subset $A$ of the state space, of the recurrence time and costs until $A$ and the quasicompactness of the {Markov} processes are replaced by the quasicompactness of the embedded {Markov} processes on $A$."},
	Author = {Wijngaard, Jacob},
	Date-Added = {2007-07-15 12:25:19 -0500},
	Date-Modified = {2007-07-15 12:26:11 -0500},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Keywords = {MDP},
	Mrclass = {90C40},
	Mrnumber = {MR0525902 (58 \#26029)},
	Number = {1},
	Pages = {91--102},
	Title = {Stationary {M}arkovian decision problems and perturbation theory of quasi-compact linear operators},
	Volume = {2},
	Year = {1977}}

@article{wes77,
	Annote = { A {Markov} decision process is considered in discrete time, countable state space, and general decision space. Total expected reward is to be optimized by choice of a strategy. The optimum strategy is found using the fixed point of a contraction mapping on a Banach space with a weighted supremum norm. This approach allows some earlier hypotheses to be weakened. Inequality bounds are obtained for the optimal reward, and also an algorithm to calculate it.},
	Author = {Wessels, J.},
	Date-Added = {2007-07-15 12:24:39 -0500},
	Date-Modified = {2007-07-15 12:25:07 -0500},
	Fjournal = {Journal of Mathematical Analysis and Applications},
	Issn = {0022-247x},
	Journal = JMAA,
	Keywords = {MDP},
	Mrclass = {90C40},
	Mrnumber = {MR0441363 (55 \#14226)},
	Mrreviewer = {Bruce D. Craven},
	Number = {2},
	Pages = {326--335},
	Title = {Markov programming by successive approximations with respect to weighted supremum norms},
	Volume = {58},
	Year = {1977}}

@article{har72,
	Annote = {
 The author investigates countable state and action {Markov} decision processes in which the objective is to maximize the expected discounted reward. He replaces the assumption of bounded rewards by weaker conditions. His main result is that there exists a stationary $\varepsilon$-optimal policy for every $\varepsilon>0$ and that there exists a stationary optimal policy in the finite action case.},
	Author = {Harrison, J. M.},
	Date-Added = {2007-07-15 12:23:41 -0500},
	Date-Modified = {2007-07-15 12:24:09 -0500},
	Fjournal = {Annals of Mathematical Statistics},
	Issn = {0003-4851},
	Journal = ANNMS,
	Mrclass = {90C99},
	Mrnumber = {MR0354023 (50 \#6505)},
	Mrreviewer = {V. M. Docviri},
	Pages = {636--644},
	Title = {Discrete dynamic programming with unbounded rewards},
	Volume = {43},
	Year = {1972}}

@book{frewen84,
	Address = {New York},
	Annote = {hui},
	Author = {Freidlin, M.I. and Wentzell, A .D.},
	Date-Added = {2007-07-11 11:01:23 -0400},
	Date-Modified = {2007-07-11 11:01:41 -0400},
	Note = {Series in Comprehensive Studies in Mathematics},
	Publisher = {Springer},
	Title = {Random Perturbations of Dynamical Systems},
	Year = 1984}

@book{capmoubyd05,
	Address = {Secaucus, NJ, USA},
	Author = {Capp\'{e}, Olivier and Moulines, Eric and Ryden, Tobias},
	Date-Added = {2007-07-10 22:15:28 -0400},
	Date-Modified = {2008-06-29 21:22:46 -0500},
	Isbn = {0387402640},
	Keywords = {bayesian, estimation, inference, likelihood, markov, metropolis-hastings},
	Publisher = {Springer-Verlag New York, Inc.},
	Series = {Springer Series in Statistics},
	Title = {Inference in Hidden {Markov} Models},
	Year = {2005}}

@article{demkon02,
	Author = {Dembo, A. and Kontoyiannis, I.},
	Date-Added = {2007-07-10 21:32:18 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TIT,
	Month = {June},
	Pages = {1590-1615},
	Title = {Source coding, large deviations, and approximate pattern matching},
	Volume = {48},
	Year = {2002}}

@book{lanmey06,
	Address = {Princeton, NJ, USA},
	Author = {Langville, Amy N. and Meyer, Carl D.},
	Date-Added = {2007-06-17 12:23:51 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0691122024},
	Publisher = {Princeton University Press},
	Title = {Google's PageRank and Beyond: The Science of Search Engine Rankings},
	Year = {2006}}

@book{big94,
	Author = {Biggs, N. and Biggs, N.L.},
	Date-Added = {2007-06-17 12:21:44 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Cambridge University Press},
	Title = {{Algebraic Graph Theory}},
	Year = {1994}}

@article{deuhuifissch00,
	Annote = {hui},
	Author = {Deuflhard, P. and Huisinga, W. and Fischer, A. and Sch\"utte, C.},
	Date-Added = {2007-06-17 12:16:35 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Lin. Alg. Appl.},
	Pages = {39--59},
	Title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled {M}arkov Chains},
	Volume = 315,
	Year = 2000}

@article{boveckgaykle00,
	Author = {Bovier, Anton and Eckhoff, Michael and Gayrard, V\'eronique and Klein, Markus},
	Coden = {JPHAC5},
	Date-Added = {2007-06-17 12:13:55 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Physics. A. Mathematical and General},
	Issn = {0305-4470},
	Journal = {J. Phys. A},
	Mrclass = {82C31 (60J10)},
	Mrnumber = {2001k:82080},
	Number = {46},
	Pages = {L447--L451},
	Title = {Metastability and small eigenvalues in {M}arkov chains},
	Volume = {33},
	Year = {2000}}

@article{senver66a,
	Author = {Seneta, E. and Vere-Jones, D.},
	Date-Added = {2007-06-17 12:07:09 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = JAP,
	Pages = {403--434},
	Title = {On quasi-stationary distributions in discrete-time {M}arkov chains with a denumerable infinity of states},
	Volume = {3},
	Year = {1966}}

@article{ferkesmar96,
	Author = {Ferrari, P. A. and Kesten, H. and Mart\'inez, S.},
	Date-Added = {2007-06-17 12:05:57 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNAP,
	Pages = {577-616},
	Title = {{$R$}-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata},
	Volume = {6},
	Year = {1996}}

@article{krimoo93,
	Author = {Krishnamurthy, V. and Moore, J. B.},
	Date-Added = {2007-05-15 17:21:58 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TSP,
	Number = {8},
	Pages = {2557-2573},
	Title = {On-line estimation of hidden {M}arkov model parameters based on the {K}ullback-{L}eibler information measure},
	Volume = {41},
	Year = {1993}}

@unpublished{LMD07,
	Author = {Arienti, M. and Mathew, G. and Meyn, S. P. and Pasini, J-M. and Smith, T. and West, M.},
	Date-Added = {2007-05-14 20:37:12 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {{In preparation}},
	Title = {Learning macroscopic dynamics},
	Year = {2007}}

@article{givkupstu04,
	Author = {Givon, D. and Kupferman, R. and Stuart, A.},
	Date-Added = {2007-05-14 20:26:25 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Nonlinearity},
	Number = {6},
	Pages = {R55-R127},
	Title = {Extracting macroscopic dynamics: model problems and algorithms},
	Volume = {17},
	Year = {2004}}

@article{deljun99,
	Author = {Dellnitz, Michael and Junge, Oliver},
	Date-Added = {2007-05-02 14:01:30 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {SIAM J.~Num.~Anal.},
	Number = 2,
	Pages = {491--515},
	Title = {On the approximation of complicated dynamical behavior},
	Volume = 36,
	Year = 1999}

@article{sha48,
	Author = {Shannon, C.E.},
	Date-Added = {2007-04-26 07:30:06 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Bell System Tech. J.},
	Pages = {379-423, 623-656},
	Title = {A mathematical theory of communication},
	Volume = {27},
	Year = {1948}}

@article{robmon51a,
	Author = {Robbins, H. and Monro, S.},
	Date-Added = {2007-04-18 16:53:11 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Annals of Mathematical Statistics},
	Pages = {400--407},
	Title = {A Stochastic Approximation Method},
	Volume = {22},
	Year = {1951}}

@article{kevgeahum04,
	Author = {Kevrekidis, I. G. and Gear, C. W. and Hummer, G.},
	Date-Added = {2007-04-18 16:17:34 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {A. I. Ch. E. Journal},
	Pages = {1346--1354},
	Title = {Equation-free: the computer-assisted analysis of complex, multiscale systems},
	Volume = {50},
	Year = {2004}}

@inproceedings{fro01,
	Author = {Froyland, G.},
	Booktitle = {Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998},
	Date-Added = {2007-04-16 17:12:21 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Mees, Alistair},
	Pages = {283-324},
	Publisher = {Birkhauser},
	Title = {Extracting dynamical behaviour via {Markov} models},
	Year = {2001}}

@article{bra98b,
	Author = {Brandiere, O.},
	Date-Added = {2007-04-16 11:34:02 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Pages = {1293-1314},
	Title = {Some pathological traps for stochastic approximation},
	Volume = {36},
	Year = {1998}}

@article{mor65,
	Author = {Mori, H.},
	Date-Added = {2007-04-14 16:21:27 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Progress of Theoretical Physics},
	Pages = {423-455},
	Title = {Transport, Collective Motion, and Brownian Motion},
	Volume = {33},
	Year = {1965}}

@book{zwa01,
	Address = {Oxford, England},
	Author = {Zwanzig, R.},
	Date-Added = {2007-04-14 16:21:27 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Oxford University Press},
	Title = {Nonequilibrium Statistical Mechanics},
	Year = {2001}}

@article{amakevmar06,
	Author = {Amat, Miguel A. and Kevrekidis, I. G. and Maroudas, D.},
	Date-Added = {2007-04-14 16:21:27 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Physical Review B},
	Pages = {132201},
	Title = {Coarse Molecular-Dynamics Determination of the Onset of Structural Transitions: Melting of Crystalline Solids},
	Volume = {74},
	Year = {2006}}

@article{cho03,
	Abstract = {In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in complex systems through integration of unwanted scales. We establish the relation between these methods for systems in thermal equilibrium, and use this relation to find renormalization parameter flows and the coefficients in reduced systems by expanding conditional expectations in series and evaluating the coefficients by Monte-Carlo. We illustrate the construction by finding parameter flows for simple spin systems and then using the renormalized (=reduced) systems to calculate the critical temperature and the magnetization.
},
	Author = {Chorin, A. J.},
	Date-Added = {2007-04-14 16:20:38 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = JMMS,
	Number = {1},
	Pages = {105--118},
	Title = {Conditional Expectations and Renormalization},
	Volume = {1},
	Year = {2003}}

@article{sonshr89,
	Address = {Philadelphia, PA, USA},
	Author = {Soner, H. M. and Shreve, S. E.},
	Date-Added = {2007-04-14 13:41:38 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Doi = {http://dx.doi.org/10.1137/0327047},
	Issn = {0363-0129},
	Journal = SICON,
	Number = {4},
	Pages = {876--907},
	Publisher = {Society for Industrial and Applied Mathematics},
	Title = {Regularity of the value function for a two-dimensional singular stochastic control problem},
	Volume = {27},
	Year = {1989},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/0327047}}

@book{yinzha98,
	Address = {New York, NY, USA},
	Author = {Yin, G. George and Zhang, Qing},
	Date-Added = {2007-04-12 21:56:44 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-387-98244-2},
	Publisher = {Springer-Verlag New York, Inc.},
	Title = {Continuous-time {Markov} chains and applications: a singular perturbation approach},
	Year = {1998}}

@book{bil95,
	Address = {New York},
	Author = {Billingsley, P.},
	Date-Added = {2007-03-30 18:13:52 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {John Wiley \& Sons},
	Title = {{Probability and Measure}},
	Year = {1995}}

@book{leichielblaamarschschske06,
	Address = {Secaucus, NJ, USA},
	Author = {Leimkuhler, Benedict and Chipot, Christophe and Elber, Ron and Laaksonen, Aatto and Mark, Alan and Schlick, Tamar and Sch\&\#252;tte, Christoph and Skeel, Robert},
	Date-Added = {2007-03-27 21:14:22 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {3540255427},
	Publisher = {Springer-Verlag New York, Inc.},
	Title = {New Algorithms for Macromolecular Simulation (Lecture Notes in Computational Science and Engineering)},
	Year = {2006}}

@book{shr04b,
	Address = {New York},
	Author = {Shreve, S. E.},
	Date-Added = {2007-03-25 14:14:02 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Continuous-time models},
	Publisher = {Springer-Verlag},
	Series = {Springer Finance},
	Title = {Stochastic Calculus for Finance {II}: Continuous-Time Models},
	Year = {2004}}

@book{shr04a,
	Address = {New York},
	Author = {Shreve, S. E.},
	Date-Added = {2007-03-25 14:14:02 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Continuous-time models},
	Publisher = {Springer-Verlag},
	Series = {Springer Finance},
	Title = {Stochastic Calculus for Finance {I}: The Binomial Asset Pricing Model},
	Year = {2004}}

@article{ade04a,
	Author = {Adelman, D.},
	Date-Added = {2007-03-14 20:29:10 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = OR,
	Number = {4},
	Pages = {499--514},
	Title = {A price-directed approach to stochastic inventory/routing},
	Volume = {52},
	Year = {2004}}

@book{ber07a,
	Author = {Bertsekas, D. P.},
	Date-Added = {2007-03-11 18:25:56 -0400},
	Date-Modified = {2008-01-21 23:08:57 -0500},
	Edition = {Third},
	Isbn = {1-886529-08-6},
	Publisher = {Athena Scientific},
	Title = {Dynamic Programming and Optimal Control},
	Year = {2007}}

@article{bertsi91a,
	Author = {Bertsekas, D. P. and Tsitsiklis, J. N.},
	Date-Added = {2007-03-11 18:12:53 -0400},
	Date-Modified = {2008-01-21 23:11:08 -0500},
	Fjournal = {Mathematics of Operations Research},
	Journal = MOR,
	Number = {3},
	Pages = {580--595},
	Title = {An analysis of stochastic shortest path problems},
	Volume = {16},
	Year = {1991}}

@article{den67,
	Author = {Denardo, E.},
	Date-Added = {2007-03-11 18:00:57 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {SIAM Review},
	Pages = {165--177},
	Title = {Contraction Mappings Underlying the Theory of Dynamic Programming},
	Volume = {9},
	Year = {1967}}

@article{vei69,
	Author = {{A.F. Veinott, Jr.}},
	Date-Added = {2007-03-11 17:46:19 -0400},
	Date-Modified = {2011-01-29 09:30:04 -0600},
	Journal = ANNMS,
	Number = {5},
	Pages = {1635-1660},
	Title = {Discrete dynamic programming with sensitive discount optimality criteria},
	Volume = {40},
	Year = {1969}}

@article{tatmit06,
	Adsnote = {Provided by the Smithsonian/NASA Astrophysics Data System},
	Author = {{Tatikonda}, S. and {Mitter}, S.},
	Date-Added = {2007-02-19 11:04:22 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Eprint = {cs/0609139},
	Journal = {ArXiv Computer Science e-prints},
	Month = {September},
	Title = {The Capacity of Channels with Feedback},
	Year = {2006}}

@article{ranjun04,
	Abstract = { It is well known that in estimating performance measures associated with a stochastic system a good importance sampling distribution (IS) can give orders of magnitude of variance reduction while a bad one may lead to large, even infinite, variance. In this paper we study how this sensitivity of the estimator variance to the importance sampling change of measure may be "dampened" by combining importance sampling with stochastic approximation based temporal difference (TD) method. We consider a finite state space discrete time {Markov} chain (DTMC) with one-step transition rewards and an absorbing set of states and focus on estimating the cumulative expected reward to absorption starting from any state. In this setting we develop sufficient conditions under which the estimate resulting from the combined approach has a mean square error that asymptotically equals zero even when the estimate formed by using only importance sampling change of measure has infinite variance. In particular, we consider the problem of estimating the small buffer overflow probability in a queuing network, where the change of measure suggested in literature is shown to have infinite variance under certain parameters and where the appropriate combination of IS and TD method can be empirically seen to have a much faster convergence rate compared to naive simulation.},
	Address = {New York, NY, USA},
	Author = {Randhawa, R. S. and Juneja, S.},
	Date-Added = {2007-02-15 20:53:02 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Doi = {http://doi.acm.org/10.1145/974734.974735},
	Issn = {1049-3301},
	Journal = {ACM Trans. Model. Comput. Simul.},
	Number = {1},
	Pages = {1--30},
	Publisher = {ACM Press},
	Title = {Combining importance sampling and temporal difference control variates to simulate {Markov} Chains},
	Volume = {14},
	Year = {2004},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/974734.974735}}

@article{morlee99,
	Author = {Morari, M. and Lee, J.H.},
	Date-Added = {2007-02-15 19:46:08 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Computers \&\ Chemical Engineering},
	Number = {4},
	Pages = {667--682},
	Title = {Model predictive control: Past, present and future},
	Url = {http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=1641},
	Volume = {23},
	Year = {1999},
	Bdsk-Url-1 = {http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=1641}}

@incollection{schhuimey03,
	Address = {Dordrecht},
	Author = {Sch{\"u}tte, C. and Huisinga, W. and Meyn, S.},
	Booktitle = {IUTAM Symposium on Nonlinear Stochastic Dynamics},
	Date-Added = {2007-01-24 09:58:50 -0800},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {60J60},
	Mrnumber = {MR2049398 (2004m:60172)},
	Pages = {71--81},
	Publisher = {Kluwer Acad. Publ.},
	Series = {Solid Mech. Appl.},
	Title = {Metastability of diffusion processes},
	Volume = {110},
	Year = {2003}}

@book{res92a,
	Address = {Boston, MA},
	Author = {Resnick, S.},
	Date-Added = {2006-12-15 16:39:44 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-8176-3591-2},
	Mrclass = {60-01 (60J10 60J27 60K05)},
	Mrnumber = {MR1181423 (93m:60004)},
	Mrreviewer = {Richard F. Serfozo},
	Pages = {xii+626},
	Publisher = {Birkh\"auser Boston Inc.},
	Title = {Adventures in stochastic processes},
	Year = {1992}}

@article{brabar96,
	Address = {Hingham, MA, USA},
	Author = {Bradtke, S. J. and Barto, A. G.},
	Date-Added = {2006-12-11 08:28:22 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Doi = {http://dx.doi.org/10.1007/BF00114723},
	Issn = {0885-6125},
	Journal = {Mach. Learn.},
	Number = {1-3},
	Pages = {33--57},
	Publisher = {Kluwer Academic Publishers},
	Title = {Linear least-squares algorithms for temporal difference learning},
	Volume = {22},
	Year = {1996},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00114723}}

@article{bar86,
	Author = {Barron, A. R.},
	Date-Added = {2006-12-09 13:17:53 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNP,
	Number = {1},
	Pages = {336 - 342},
	Title = {Entropy and the {C}entral {L}imit {T}heorem},
	Volume = {14},
	Year = {1986}}

@article{shi93a,
	Author = {Shimkin, N.},
	Coden = {AAPBBD},
	Date-Added = {2006-12-07 19:25:14 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Advances in Applied Probability},
	Issn = {0001-8678},
	Journal = AAP,
	Mrclass = {60F10 (62F03 90C15)},
	Mrnumber = {MR1241933 (94h:60034)},
	Mrreviewer = {Iosif Pinelis},
	Number = {4},
	Pages = {875--894},
	Title = {Extremal large deviations in controlled i.i.d.\ processes with applications to hypothesis testing},
	Volume = {25},
	Year = {1993}}

@article{mantsi05a,
	Abstract = {This paper considers a {Markov} decision process (MDP) that can be defined by a triplet $(\scr{S},\scr{A},{\rm P})$ where $\scr{S}$ and $\scr{A}$ are the state and the action spaces, respectively, and ${\rm P}$ is the transition probability, that is, ${\rm P}(s'|s,a)$ is the probability that the next state of the process is $s'$, given that the current state is $s$ and that action $a$ was taken. The spaces $\scr{S}$ and $\scr{A}$ are both finite. It is shown that, under a suitable communicating condition, the set of the MDP's limiting expected state-action frequencies (also known as state-action occupation measures) coincides with a polytope ${\rm X}$, defined as the set of probability measures $x$ on $\scr{S}\times\scr{A}$ that satisfy $$ \sum_s\sum_a {\rm P}(s'|s,a)x(s,a)=\sum_{a'} x(s',a') \quad\forall\;s'\in\scr{S}. $$ It is also shown that the probability of exceeding a given distance between the empirical frequency distribution and the polytope decays exponentially with time under every decision policy. Similar results are obtained for the empirical rewards},
	Author = {Mannor, S. and Tsitsiklis, J. N.},
	Date-Added = {2006-12-07 19:23:54 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C40 (60B10 60F10)},
	Mrnumber = {MR2161197 (2006d:90211)},
	Mrreviewer = {O. Hern{\'a}ndez Lerma},
	Number = {3},
	Pages = {545--561},
	Title = {On the empirical state-action frequencies in {M}arkov decision processes under general policies},
	Volume = {30},
	Year = {2005}}

@inproceedings{gam99a,
	Abstract = {Extension of the PAC framework to finite and countable {Markov} chains. (English summary) Proceedings of the Twelfth Annual Conference on Computational Learning Theory (Santa Cruz, CA, 1999), 308--317 (electronic), ACM, New York, 1999.
},
	Address = {New York},
	Author = {Gamarnik, D.},
	Booktitle = {Proceedings of the Twelfth Annual Conference on Computational Learning Theory (Santa Cruz, CA, 1999)},
	Date-Added = {2006-12-07 19:21:48 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {68Q32 (68T05 90C15)},
	Mrnumber = {MR1811628},
	Pages = {308--317 (electronic)},
	Publisher = {ACM},
	Title = {Extension of the {PAC} framework to finite and countable {M}arkov chains},
	Year = {1999}}

@book{gooserded05,
	Address = {London},
	Author = {Goodwin, G. C. and Seron, M. M. and De Don\'{a}, J. A.},
	Date-Added = {2006-11-26 17:34:56 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Springer-Verlag},
	Series = {Communications and Control Engineering},
	Title = {Constrained control and estimation. An optimisation approach},
	Year = {2005}}

@book{kus84a,
	Address = {Cambridge, MA},
	Author = {Kushner, H. J.},
	Date-Added = {2006-11-22 17:51:37 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrnumber = {MR741469 (86a:60086)},
	Mrreviewer = {S. R. S. Varadhan},
	Pages = {xvii+269},
	Publisher = {MIT Press},
	Series = {MIT Press Series in Signal Processing, Optimization, and Control, 6},
	Title = {Approximation and weak convergence methods for random processes, with applications to stochastic systems theory},
	Year = {1984}}

@book{kokorekha86,
	Abstract = {From the Publisher:
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.

This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.},
	Address = {Orlando, FL, USA},
	Author = {Kokotovic, P. V. and O'Reilly, J. and Khalil, J. K.},
	Date-Added = {2006-10-10 02:23:15 +0200},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0124176356},
	Publisher = {Academic Press, Inc.},
	Title = {Singular Perturbation Methods in Control: Analysis and Design},
	Year = {1986}}

@article{RLTmemorial,
	Author = {Dunsmuir, W. T. M. and Meyn, S. P. and Roberts, G.},
	Coden = {JPRBAM},
	Date-Added = {2006-10-10 02:18:49 +0200},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Applied Probability},
	Issn = {0021-9002},
	Journal = JAP,
	Mrclass = {01A70 (60-03 60Jxx 60Kxx)},
	Mrnumber = {2003c:01047},
	Number = {2},
	Pages = {441--454},
	Title = {Obituary: {R}ichard {L}ewis {T}weedie},
	Volume = {39},
	Year = {2002}}

@article{azu67,
	Author = {Azuma, K.},
	Date-Added = {2006-09-14 18:48:25 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {T{\^o}hoku Math. Journal},
	Pages = {357--367},
	Title = {Weighted sums of certain dependent random variables},
	Volume = {19},
	Year = {1967}}

@article{bor94,
	Author = {Borkar, V. S.},
	Date-Added = {2006-09-11 18:48:32 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Pages = {176-186},
	Title = {Ergodic control of {Markov} Chains with constraints the general case},
	Volume = {32},
	Year = {1994}}

@book{lerlas99a,
	Address = {Berlin, Germany},
	Author = {Hern{\'a}ndez-Lerma, O. and Lasserre, J. B.},
	Date-Added = {2006-09-09 18:58:23 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Springer-Verlag},
	Series = {Stochastic Modeling and Applied Probability},
	Title = {Further Topics on Discrete-Time {Markov} Control Processes},
	Year = {1999}}

@article{dan55,
	Author = {Dantzig, G. B.},
	Date-Added = {2006-09-09 18:40:05 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = MS,
	Month = {April-July},
	Number = {3},
	Pages = {197-206},
	Title = {Linear Programming Under Uncertainty},
	Volume = {7},
	Year = {1995}}

@article{fedhortij79,
	Author = {Federgruen, A. and Hordijk, A. and Tijms, H. C.},
	Coden = {STOPB7},
	Date-Added = {2006-09-09 09:31:53 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Stochastic Processes and their Applications},
	Issn = {0304-4149},
	Journal = SPA,
	Mrclass = {90C40},
	Mrnumber = {MR548842 (81b:90150)},
	Mrreviewer = {S. K. Srinivasan},
	Number = {2},
	Pages = {223--235},
	Title = {Denumerable state semi-{M}arkov decision processes with unbounded costs, average cost criterion unbounded costs, average cost criterion},
	Volume = {9},
	Year = {1979}}

@article{altspi95,
	Author = {Altman, E. and Spieksma, F.},
	Date-Added = {2006-09-08 23:06:18 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ZOR,
	Number = {2},
	Pages = {169-188},
	Title = {The Linear Program approach in {Markov} Decision Problems revisited},
	Volume = {42},
	Year = {1995}}

@article{bor84,
	Author = {Borkar, V. S.},
	Date-Added = {2006-09-08 22:40:19 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Number = {6},
	Pages = {965--978},
	Title = {On minimum cost per unit time control of {Markov} chains},
	Volume = {22},
	Year = {1984}}

@article{bor83a,
	Abstract = {Controlled {Markov} chains with average cost criterion and with special cost and transition structures are studied. Existence of optimal stationary strategies is established for the average cost criterion. Corresponding dynamic programming equations are derived. A stochastic network problem that includes interconnected queues as a special case is described and studied within this framework.
},
	Author = {Borkar, V. S.},
	Date-Added = {2006-09-08 22:39:11 -0400},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Keywords = {optimal control; average cost; dynamic programming; stochastic networks},
	Number = {4},
	Pages = {652--666},
	Title = {Controlled {Markov} chains and stochastic networks},
	Volume = {21},
	Year = {1983}}

@article{douformousou04,
	Abstract = {We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts (2001) for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings Metropolis algorithms.

},
	Author = {Douc, R. and Fort, G. and Moulines, E. and Soulier, P.},
	Date-Added = {2006-08-23 11:02:58 -0500},
	Date-Modified = {2007-12-04 09:16:41 -0600},
	Journal = ANNAP,
	Number = {3},
	Pages = {1353--1377},
	Title = {Practical drift conditions for subgeometric rates of convergence},
	Volume = {14},
	Year = {2004}}

@book{ber05a,
	Author = {Bertsekas, D. P.},
	Date-Added = {2006-08-22 16:56:30 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Edition = {Third},
	Isbn = {1-886529-26-4},
	Mrclass = {49-01 (49L20 90-01 90C39 90C40 91B02 93-01)},
	Mrnumber = {MR2183196 (2006g:49001)},
	Pages = {xvi+543},
	Publisher = {Athena Scientific, Belmont, MA},
	Title = {Dynamic programming and optimal control. {V}ol. {I}},
	Year = {2005}}

@unpublished{krulehramshr06,
	Author = {Kruk, L. and Lehoczky, J. and Ramanan, K. and Shreve, S.},
	Date-Added = {2006-08-22 16:54:35 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Month = {March},
	Note = {Submitted for publication},
	Title = {An Explicit Formula for the Skorohod Map on [0,a]},
	Year = {2006}}

@book{bor91,
	Address = {Longman Scientific \&\ Technical, UK},
	Author = {Borkar, V. S.},
	Date-Added = {2006-08-22 16:41:39 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Pitman Research Notes in Mathematics Series \# 240},
	Title = {{Topics in controlled {Markov} chains}},
	Year = {1991}}

@book{feishw02a,
	Address = {Boston, MA},
	Date-Added = {2006-08-22 16:26:06 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Feinberg, E. A. and Shwartz, A.},
	Isbn = {0-7923-7459-2},
	Mrclass = {90-00 (60J10 90C15 90C40 93E20)},
	Mrnumber = {MR1887198 (2003a:90001)},
	Mrreviewer = {M. Iosifescu},
	Note = {Methods and applications},
	Pages = {viii+565},
	Publisher = {Kluwer Academic Publishers},
	Series = {International Series in Operations Research \& Management Science, 40},
	Title = {Handbook of {M}arkov decision processes},
	Year = {2002}}

@book{alt99,
	Author = {Altman, E.},
	Date-Added = {2006-08-22 16:23:58 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {xii+242},
	Publisher = {Chapman \& Hall/CRC, Boca Raton, FL},
	Series = {Stochastic Modeling},
	Title = {Constrained {M}arkov decision processes},
	Year = {1999}}

@book{dubsav65,
	Address = {New York},
	Author = {Dubins, Lester E. and Savage, Leonard J.},
	Date-Added = {2006-08-22 16:21:38 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {60.40},
	Mrnumber = {MR0236983 (38 \#5276)},
	Mrreviewer = {M. Iosifescu},
	Pages = {xiv+249},
	Publisher = {McGraw-Hill Book Co.},
	Title = {How to gamble if you must. {I}nequalities for stochastic processes},
	Year = {1965}}

@book{dynys79a,
	Address = {Berlin},
	Author = {Dynkin, E. B. and Yushkevich, A. A.},
	Date-Added = {2006-08-22 16:17:22 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {3-540-90387-9},
	Mrclass = {90C40},
	Mrnumber = {MR554083 (80k:90037)},
	Note = {Translated from the Russian original by J. M. Danskin and C. Holland},
	Pages = {xvii+289},
	Publisher = {Springer-Verlag},
	Series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]},
	Title = {Controlled {M}arkov processes},
	Volume = {235},
	Year = {1979}}

@article{bor89b,
	Author = {Borkar, V. S.},
	Coden = {SJCODE},
	Date-Added = {2006-08-22 16:00:32 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {SIAM Journal on Control and Optimization},
	Issn = {0363-0129},
	Journal = SICON,
	Keywords = {Markov chain; optimal control; dynamic programming},
	Mrclass = {90C40 (60J10 93E20)},
	Mrnumber = {MR993291 (90e:90142)},
	Number = {3},
	Pages = {642--657},
	Title = {Control of {Markov} chains with long-run average cost criterion: the dynamic programming equations},
	Volume = {27},
	Year = {1989}}

@incollection{bor02a,
	Address = {Boston, MA},
	Author = {Borkar, V. S.},
	Booktitle = {Handbook of {Markov} decision processes},
	Date-Added = {2006-08-22 15:56:00 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {90C40 (90C29 90C46)},
	Mrnumber = {MR1887208},
	Pages = {347--375},
	Publisher = {Kluwer Acad. Publ.},
	Series = {Internat. Ser. Oper. Res. Management Sci.},
	Title = {Convex analytic methods in {M}arkov decision processes},
	Volume = {40},
	Year = {2002}}

@article{bhabor05a,
	Author = {Bhatt, Abhay G. and Borkar, V. S.},
	Date-Added = {2006-08-22 15:52:16 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Sankhy\=a. The Indian Journal of Statistics},
	Issn = {0972-7671},
	Journal = {Sankhy\=a},
	Mrclass = {90C40 (60J25 93E20)},
	Mrnumber = {MR2203886 (2006j:90116)},
	Mrreviewer = {Quan Xin Zhu},
	Number = {1},
	Pages = {1--18},
	Title = {Existence of optimal {M}arkov solutions for ergodic control of {M}arkov processes},
	Volume = {67},
	Year = {2005},
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@book{mck05,
	Author = {McKean, H. P.},
	Date-Added = {2006-08-09 12:10:57 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-8218-3887-3},
	Mrclass = {60-02 (60H05 60H10 60H20)},
	Mrnumber = {MR2169626 (2006d:60003)},
	Note = {Reprint of the 1969 edition, with errata},
	Pages = {xvi+141},
	Publisher = {AMS Chelsea Publishing, Providence, RI},
	Title = {Stochastic integrals},
	Year = {2005}}

@book{kelmck73,
	Address = {Providence, R.I.},
	Booktitle = {SIAM-AMS Proceedings, Vol. VI},
	Date-Added = {2006-08-09 12:10:57 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Keller, J. B. and McKean, H. P.},
	Mrclass = {60-06 (60HXX)},
	Mrnumber = {MR0336771 (49 \#1544)},
	Pages = {v+209},
	Publisher = {American Mathematical Society},
	Title = {Stochastic differential equations},
	Year = {1973}}

@article{haj85,
	Author = {Hajek, B.},
	Date-Added = {2006-08-08 13:42:47 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Journal = MOR,
	Number = {4},
	Pages = {543--556},
	Title = {Extremal splittings of point processes},
	Volume = {10},
	Year = {1985}}

@article{altkonliu92,
	Author = {Altman, E. and Konstantopoulos, P. and Liu, Z.},
	Date-Added = {2006-08-08 13:41:38 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = QS,
	Pages = {35-57},
	Title = {Stability, Monotonicity and Invariant Quantities in General Polling Systems},
	Volume = {11},
	Year = {1992}}

@article{altgauhor00,
	Author = {Altman, E. and Gaujal, B. and Hordijk, A.},
	Date-Added = {2006-08-08 13:40:53 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Journal = MOR,
	Number = {2},
	Pages = {324--347},
	Title = {Multimodularity, convexity, and optimization properties},
	Volume = {25},
	Year = {2000}}

@article{mur05,
	Author = {Murota, K.},
	Date-Added = {2006-08-08 13:40:38 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C10 (90B06 90C25 90C35)},
	Mrnumber = {MR2161202 (2006d:90102)},
	Mrreviewer = {Anna Rycerz},
	Number = {3},
	Pages = {658--661},
	Title = {Note on multimodularity and {$L$}-convexity},
	Volume = {30},
	Year = {2005}}

@article{putbru79b,
	Author = {Puterman, M. L. and Brumelle, S. L.},
	Date-Added = {2006-08-07 17:28:19 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C39},
	Mrnumber = {MR543609 (80k:90036)},
	Mrreviewer = {R. N. Kaul},
	Number = {1},
	Pages = {60--69},
	Title = {On the convergence of policy iteration in stationary dynamic programming},
	Volume = {4},
	Year = {1979}}

@incollection{putbru79,
	Address = {New York},
	Author = {Puterman, M. L. and Brumelle, S. L.},
	Booktitle = {Dynamic programming and its applications (Proc. Conf., Univ. British Columbia, Vancouver, B.C., 1977)},
	Date-Added = {2006-08-07 17:28:19 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {90C48},
	Mrnumber = {MR537876 (80i:90097)},
	Mrreviewer = {Mary W. Cooper},
	Pages = {91--113},
	Publisher = {Academic Press},
	Title = {The analytic theory of policy iteration},
	Year = {1978}}

@phdthesis{spi90a,
	Address = {PO Box 9500 2300 RA Leiden, The Netherlands.},
	Author = {Spieksma, F. M.},
	Date-Added = {2006-08-07 17:23:09 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	School = {Leiden University},
	Title = {Geometrically Ergodic {Markov} Chains and the Optimal Control of Queues},
	Year = {1990}}

@article{whi63,
	Author = {White, D. J.},
	Date-Added = {2006-08-01 12:16:07 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Mathematical Analysis and Applications},
	Journal = JMAA,
	Pages = {373--376},
	Title = {Dynamic programming, {M}arkov chains, and the method of successive approximations.},
	Volume = {6},
	Year = {1963}}

@article{bax05,
	Author = {Baxendale, P. H.},
	Date-Added = {2006-08-01 12:08:23 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {The Annals of Applied Probability},
	Journal = AAP,
	Number = {1B},
	Pages = {700--738},
	Title = {Renewal theory and computable convergence rates for geometrically ergodic {M}arkov chains},
	Volume = {15},
	Year = {2005},
	Bdsk-File-1 = {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}}

@article{ros95b,
	Author = {Rosenthal, J. S.},
	Date-Added = {2006-08-01 12:01:19 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of the American Statistical Association},
	Journal = JASA,
	Number = {431},
	Pages = {1136},
	Title = {Correction: ``{M}inorization conditions and convergence rates for {M}arkov chain {M}onte {C}arlo''},
	Volume = {90},
	Year = {1995}}

@article{ros95a,
	Author = {Rosenthal, J. S.},
	Date-Added = {2006-08-01 12:01:19 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of the American Statistical Association},
	Journal = JASA,
	Number = {430},
	Pages = {558--566},
	Title = {Minorization conditions and convergence rates for {M}arkov chain {M}onte {C}arlo},
	Volume = {90},
	Year = {1995}}

@book{bertsi89b,
	Address = {Upper Saddle River, NJ, USA},
	Author = {Bertsekas, D. P. and Tsitsiklis, J. N.},
	Date-Added = {2006-08-01 11:52:21 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-13-648700-9},
	Publisher = {Prentice-Hall, Inc.},
	Title = {Parallel and distributed computation: numerical methods},
	Year = {1989}}

@article{tse90a,
	Author = {Tseng, P.},
	Date-Added = {2006-08-01 11:52:05 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Operations Research Letters},
	Journal = ORL,
	Number = {5},
	Pages = {287--297},
	Title = {Solving {$H$}-horizon, stationary {M}arkov decision problems in time proportional to {$\log(H)$}},
	Volume = {9},
	Year = {1990}}

@article{ber98a,
	Author = {Bertsekas, D. P.},
	Date-Added = {2006-08-01 11:42:18 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {SIAM Journal on Control and Optimization},
	Journal = SICON,
	Number = {2},
	Pages = {742--759 (electronic)},
	Title = {A new value iteration method for the average cost dynamic programming problem},
	Volume = {36},
	Year = {1998}}

@inproceedings{panmeyven04b,
	Author = {Huang, J. and Pandit, C. and Meyn, S. P. and Veeravalli, V. V.},
	Booktitle = {In Proc. IEEE Information Theory Workshop, San Antonio, TX},
	Date-Added = {2006-07-31 12:08:21 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Keywords = {Information Theory},
	Month = {October 24-29},
	Pages = {76-81},
	Title = {Extremal Distributions in Information Theory and Hypothesis Testing (Invited.)},
	Year = {2004}}

@article{las94a,
	Author = {Lasserre, J. B.},
	Coden = {JMANAK},
	Date-Added = {2006-07-25 19:31:46 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Mathematical Analysis and Applications},
	Issn = {0022-247X},
	Journal = JMAA,
	Mrclass = {90C40},
	Mrnumber = {MR1273444 (95e:90120)},
	Mrreviewer = {S. Kalpakam},
	Number = {1},
	Pages = {233--249},
	Title = {Average optimal stationary policies and linear programming in countable space {M}arkov decision processes countable space {M}arkov decision processes},
	Volume = {183},
	Year = {1994}}

@book{andnas87,
	Address = {Chichester},
	Author = {Anderson, E. J. and Nash, P.},
	Date-Added = {2006-07-25 19:31:04 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-471-91250-6},
	Mrclass = {90C48 (49D39 90C05)},
	Mrnumber = {MR893179 (88f:90180)},
	Mrreviewer = {B. D. Craven},
	Note = {Theory and applications, A Wiley-Interscience Publication},
	Pages = {xii+172},
	Publisher = {John Wiley \& Sons Ltd.},
	Series = {Wiley-Interscience Series in Discrete Mathematics and Optimization},
	Title = {Linear programming in infinite-dimensional spaces},
	Year = {1987}}

@article{lerlas96b,
	Author = {Hern{\'a}ndez-Lerma, O. and Lasserre, J. B.},
	Coden = {SJCODE},
	Date-Added = {2006-07-25 19:29:38 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {SIAM Journal on Control and Optimization},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {93E20 (90C40)},
	Mrnumber = {MR1372915 (96j:93071)},
	Mrreviewer = {Edward J. Anderson},
	Number = {1},
	Pages = {295--310},
	Title = {Average optimality in {M}arkov control processes via discounted-cost problems and linear programming},
	Volume = {34},
	Year = {1996}}

@article{lastij96,
	Author = {Lasserre, J. B. and Tijms, J.},
	Date-Added = {2006-07-25 19:29:08 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Probability in the Engineering and Informational Sciences},
	Issn = {0269-9648},
	Journal = {Probab. Engrg. Inform. Sci.},
	Mrclass = {60J10},
	Mrnumber = {MR1386636 (96m:60152)},
	Number = {2},
	Pages = {213--221},
	Title = {Invariant probabilities with geometric tail},
	Volume = {10},
	Year = {1996}}

@article{ritsen92a,
	Author = {Ritt, R. K. and Sennott, L. I.},
	Date-Added = {2006-07-25 19:22:12 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C40 (90B22)},
	Mrnumber = {MR1196400 (93j:90126)},
	Mrreviewer = {Mamoru Ohashi},
	Number = {4},
	Pages = {901--909},
	Title = {Optimal stationary policies in general state space {M}arkov decision chains with finite action sets},
	Volume = {17},
	Year = {1992}}

@article{cavfer96b,
	Author = {Cavazos-Cadena, Rolando and Fern{\'a}ndez-Gaucherand, Emmanuel},
	Coden = {JPRBAM},
	Date-Added = {2006-07-25 19:19:10 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Applied Probability},
	Issn = {0021-9002},
	Journal = JAP,
	Mrclass = {90C40},
	Mrnumber = {MR1416221 (97i:90106)},
	Mrreviewer = {Raimi Ajibola Kasumu},
	Number = {4},
	Pages = {986--1002},
	Title = {Value iteration in a class of average controlled {M}arkov chains with unbounded costs: necessary and sufficient conditions for pointwise convergence chains with unbounded costs: necessary and sufficient conditions for pointwise convergence},
	Volume = {33},
	Year = {1996}}

@book{whi83a,
	Address = {Chichester},
	Author = {Whittle, P.},
	Date-Added = {2006-07-04 12:49:56 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-471-10496-5},
	Mrclass = {90C39 (60-02 90-02 90C40 93E10)},
	Mrnumber = {MR710833 (85e:90062)},
	Mrreviewer = {M. H. A. Davis},
	Note = {Dynamic programming and stochastic control},
	Pages = {x+317},
	Publisher = {John Wiley \& Sons Ltd.},
	Series = {Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics},
	Title = {Optimization over time. {V}ol. {II}},
	Year = {1983}}

@book{whi82a,
	Address = {Chichester},
	Author = {Whittle, P.},
	Date-Added = {2006-07-04 12:49:56 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-471-10120-6},
	Mrclass = {90-02 (49-02 49C20 90C39 93-02)},
	Mrnumber = {MR670949 (84f:90002)},
	Mrreviewer = {M. H. A. Davis},
	Note = {Dynamic programming and stochastic control},
	Pages = {xi+317},
	Publisher = {John Wiley \& Sons Ltd.},
	Series = {Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics},
	Title = {Optimization over time. {V}ol. {I}},
	Year = {1982}}

@article{fedschtij83a,
	Author = {Federgruen, A. and Schweitzer, P. J. and Tijms, H. C.},
	Date-Added = {2006-07-04 12:46:54 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C40},
	Mrnumber = {85a:90225},
	Mrreviewer = {Jaap Wessels},
	Number = {2},
	Pages = {298--313},
	Title = {Denumerable undiscounted semi-{M}arkov decision processes with unbounded rewards},
	Volume = {8},
	Year = {1983}}

@article{panmey06a,
	Author = {Pandit, C. and Meyn, S. P.},
	Date-Added = {2006-05-03 10:52:30 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SPA,
	Keywords = {Information Theory},
	Month = {May},
	Number = {5},
	Pages = {724-756},
	Title = {Worst-Case Large-Deviations with Application to Queueing and Information Theory},
	Volume = {116},
	Year = {2006}}

@book{son98a,
	Address = {New York},
	Author = {Sontag, E. D.},
	Date-Added = {2006-04-04 18:16:52 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Edition = {Second},
	Isbn = {0-387-98489-5},
	Mrclass = {93-01 (49-01 93-02)},
	Mrnumber = {MR1640001 (99k:93001)},
	Mrreviewer = {Heinz Sch{\"a}ttler},
	Note = {Deterministic finite-dimensional systems},
	Pages = {xvi+531},
	Publisher = {Springer-Verlag},
	Series = {Texts in Applied Mathematics},
	Title = {Mathematical control theory},
	Volume = {6},
	Year = {1998}}

@article{mayrak03a,
	Author = {Mayne, D. Q. and Rakovi{\'c}, S.},
	Date-Added = {2006-04-04 18:15:54 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Computational Optimization and Applications. An International Journal},
	Journal = {Comput. Optim. Appl.},
	Note = {A tribute to Elijah (Lucien) Polak},
	Number = {1-3},
	Pages = {167--191},
	Title = {Optimal control of constrained piecewise affine discrete-time systems},
	Volume = {25},
	Year = {2003}}

@article{ste01a,
	Abstract = { Let ${X_i, i\geq0}$ be a strongly mixing Harris recurrent {Markov} chain on a state space $\scr X$, with stationary distribution $\pi$, and let $g:{\scr X}\to\bf R$ be such that $\pi(g^2)<\infty$. Then the normalized partial sums $W_k(g)\coloneq k^{-1/2}\sum^{k-1}_{j=0}{g(X_j)-\pi(g)}$ satisfy a central limit theorem as $k\to\infty$, with error of order $k^{-1/2}$ with respect to Kolmogorov distance [E. Bolthausen, Z. Wahrsch. Verw. Gebiete 60 (1982), no. 3, 283--289; MR0664418 (83j:60063)]. In this paper, under the stronger assumption of $V$-uniform ergodicity [S. P. Meyn and R. L. Tweedie, {Markov} chains and stochastic stability, Springer, London, 1993; MR1287609 (95j:60103)], it is shown that the $n$-th moment also converges, as long as $|g(x)-\pi(g)|\leq V(x)^{1/n}$ for all $x\in\scr X$, with an error bound for the approximation of $E_x{W^n_k(g)}$ of order $k^{-1/2}V(x)$.
Reviewed by Andrew D. Barbour},
	Author = {Steinsaltz, D.},
	Date-Added = {2006-04-03 12:43:28 -0500},
	Date-Modified = {2009-04-28 07:09:09 -0500},
	Fjournal = {Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series},
	Issn = {0019-3577},
	Journal = {Indag. Math. (N.S.)},
	Mrclass = {60J05 (60F05)},
	Mrnumber = {MR1908880 (2003j:60098)},
	Mrreviewer = {Andrew D. Barbour},
	Number = {4},
	Pages = {533--555},
	Title = {Convergence of moments in a {M}arkov-chain {Central Limit Theorem}},
	Volume = {12},
	Year = {2001}}

@book{yinzha05,
	Address = {New York},
	Author = {Yin, G. G. and Zhang, Q.},
	Date-Added = {2006-04-03 12:34:18 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-387-21948-X},
	Mrclass = {60-02 (60G35 60J10 62L20 62M20)},
	Mrnumber = {MR2092994 (2006d:60007)},
	Mrreviewer = {Marco Ferrante},
	Note = {Stochastic Modelling and Applied Probability},
	Pages = {xix+348},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics},
	Title = {Discrete-time {M}arkov chains: Two-time-scale methods and applications},
	Volume = {55},
	Year = {2005}}

@unpublished{jer06,
	Author = {Jerrum, Mark},
	Date-Added = {2006-04-03 12:00:39 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Month = {February 27},
	Note = {Preprint School of Informatics, University of Edinburgh},
	Title = {On the approximation of one {Markov} chain by another},
	Year = {2006}}

@article{mey06a,
	Arxiv = {math.PR/0603328},
	Author = {Meyn, S. P.},
	Date-Modified = {2009-09-14 08:37:23 +0300},
	Doi = {10.1214/105051605000000737},
	Euclid = {euclid.aoap/1141654289},
	Issn = {1050-5164},
	Journal = ANNAP,
	Number = {1},
	Pages = {310-339},
	Sici = {1050-5164(2006)16:1<310:LDAACV>2.0.CO;2-3},
	Title = {Large deviation asymptotics and control variates for simulating large functions},
	Volume = {16},
	Year = {2006},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1214/105051605000000737}}

@book{mac03a,
	Author = {MacKay, D. J. C.},
	Date-Added = {2006-01-19 09:18:49 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {available from http://www.inference.phy.cam.ac.uk/mackay/itila/},
	Publisher = {Cambridge University Press},
	Title = {Information Theory, Inference, and Learning Algorithms},
	Year = {2003}}

@unpublished{chomanmey06,
	Author = {Cho, I.-K. and Mannor, S. and Meyn, S.},
	Date-Added = {2005-12-23 14:58:38 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Invited presentation at CORS / Optimization Days Joint Conference. Montreal, May 8-10, 2006},
	Title = {Average-cost temporal difference learning and adaptive control variates},
	Url = {http://www.crt.umontreal.ca/scrojopt2006/en/},
	Year = {2006},
	Bdsk-Url-1 = {http://www.crt.umontreal.ca/scrojopt2006/en/}}

@article{vapcher71,
	Author = {Vapnik, V. N. and Chervonenkis, A. Ya.},
	Date-Added = {2005-12-22 15:19:51 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Avtomat. i Telemeh.},
	Journal = {Avtomat. i Telemeh.},
	Mrclass = {62F25},
	Mrnumber = {MR0301855 (46 \#1010)},
	Mrreviewer = {A. C. Cohen},
	Number = {2},
	Pages = {42--53},
	Title = {Theory of uniform convergence of frequencies of events to their probabilities and problems of search for an optimal solution from empirical data},
	Volume = {32},
	Year = {1971}}

@article{vapcher81,
	Author = {Vapnik, V. N. and Chervonenkis, A. Ya.},
	Date-Added = {2005-12-22 15:19:51 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Akademiya Nauk SSSR. Teoriya Veroyatnoste\u\i\ i ee Primeneniya},
	Journal = {Teor. Veroyatnost. i Primenen.},
	Number = {3},
	Pages = {543--563},
	Title = {Necessary and sufficient conditions for the uniform convergence of empirical means to their true values},
	Volume = {26},
	Year = {1981}}

@article{man60a,
	Author = {Manne, A. S.},
	Date-Added = {2005-12-05 16:45:36 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = MS,
	Number = {3},
	Pages = {259-267},
	Title = {Linear programming and sequential decisions},
	Volume = {6},
	Year = {1960}}

@article{chebla04a,
	Author = {Chen, R.C. and Blankenship, G.L.},
	Date-Added = {2005-12-05 16:25:51 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TAC,
	Number = {5},
	Pages = {699--709},
	Title = {Dynamic programming equations for discounted constrained stochastic control},
	Volume = {49},
	Year = {2004}}

@article{dub62,
	Author = {Dubins, L.E.},
	Date-Added = {2005-12-05 14:47:38 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = JMAA,
	Pages = {237--244},
	Title = {On extreme points of convex sets},
	Volume = {5},
	Year = {1962}}

@article{menmanshi05,
	Author = {Mannor, S. and Menache, I. and Shimkin, N.},
	Date-Added = {2005-12-05 07:48:53 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AOR,
	Number = {2},
	Pages = {215-238},
	Title = {Basis function adaptation in temporal difference reinforcement learning},
	Volume = {134},
	Year = {2005}}

@inproceedings{keasin00a,
	Author = {Kearns, M. and Singh, S.},
	Booktitle = {Proceedings of the 13th Annual Conference on Computational Learning Theory},
	Date-Added = {2005-12-04 16:31:51 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {142--147},
	Title = {Bias-Variance Error Bounds for Temporal Difference Updates},
	Year = {2000}}

@incollection{roy01b,
	Address = {Holland},
	Author = {Van Roy, B.},
	Booktitle = {Markov Decision Processes: Models, Methods, Directions, and Open Problems},
	Date-Added = {2005-12-04 16:23:35 -0600},
	Date-Modified = {2008-12-21 09:17:02 -0600},
	Editor = {Feinberg, E. and Shwartz, A.},
	Pages = {43--82},
	Publisher = {Kluwer},
	Title = {Neuro-Dynamic Programming: Overview and Recent Trends},
	Year = {2001}}

@incollection{berborned04,
	Author = {Bertsekas, D. P. and Borkar, V. and Nedic, A.},
	Booktitle = {Handbook of Learning and Approximate Dynamic Programming},
	Date-Added = {2005-12-04 16:20:29 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Si, J. and Barto, A. and Powell, W. and Wunsch, D.},
	Notes = {Translated from Sibirskii Matematicheskii Zhurnal, Vol.32, No.4, pp.184-203, July-August, 1991},
	Pages = {690-705},
	Publisher = {Wiley-IEEE Press, Piscataway, NJ.},
	Title = {Improved Temporal Difference Methods with Linear Function Approximation},
	Year = {2004}}

@article{nedber03a,
	Abstract = {{This paper deals with policy evaluation algorithms within the
    framework of infinite-horizon dynamic programming problems with
    discounted cost. The authors consider the discrete-time stationary
    {Markov} chain with state space $\{1,2,\dots, n\}$ and the cost
    vector $J$, given by $$J(i)= E\Biggl[\sum^\infty_{t=0} \alpha^t
    g(i_t, i_{t+ 1})/i_0= i\Biggr],$$ $i= 1,2,\dots,n$, where $i_t$
    denotes the state of the system at time $t$. The authors discuss
    two methods to calculate $J$ approximately, using simulation,
    temporal difference and linear cost function approximation. The
    first method is a new algorithm, including the use of least square
    subproblems that are solved recursively and with a diminishing
    stepsize. The second method is the $\text{LSTD}(\lambda)$ algorithm,
    proposed by Boyan (to appear in Machine Learning). They state
    convergence results for these two algorithms.}},
	Author = {Nedic, A. and Bertsekas, D.P.},
	Date-Added = {2005-12-04 16:10:43 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = DEDS,
	Language = {English},
	Number = {1-2},
	Pages = {79-110},
	Reviewer = {{M.Nisio (Osaka)}},
	Title = {Least squares policy evaluation algorithms with linear function approximation},
	Volume = {13},
	Year = {2003}}

@article{farroy03a,
	Address = {Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA},
	Author = {de Farias, D. P. and Van Roy, B.},
	Date-Added = {2005-12-04 16:04:27 -0600},
	Date-Modified = {2008-12-21 09:16:49 -0600},
	Doi = {http://dx.doi.org/10.1287/opre.51.6.850.24925},
	Issn = {0030-364X},
	Journal = OR,
	Number = {6},
	Pages = {850--865},
	Publisher = {INFORMS},
	Title = {The Linear Programming Approach to Approximate Dynamic Programming},
	Volume = {51},
	Year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1287/opre.51.6.850.24925}}

@article{barsutand83a,
	Author = {Barto, A.G. and Sutton, R.S. and Anderson, C.W.},
	Date-Added = {2005-11-29 12:41:25 -0600},
	Date-Modified = {2008-12-29 08:03:14 -0600},
	Journal = {IEEE Trans. on Systems, Man and Cybernetics},
	Pages = {835-846},
	Title = {Neuron-like elements that can solve difficult learning control problems},
	Volume = {13},
	Year = {1983}}

@article{watday92a,
	Author = {Watkins, C. J. C. H. and Dayan, P.},
	Date-Added = {2005-11-29 12:38:37 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Machine Learning},
	Number = {3-4},
	Pages = {279--292},
	Title = {{$Q$}-Learning},
	Volume = 8,
	Year = 1992}

@article{bor96b,
	Author = {Borkar, V. S.},
	Date-Added = {2005-11-29 12:35:43 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Applicationes Mathematicae},
	Issn = {1233-7234},
	Journal = {Appl. Math. (Warsaw)},
	Mrclass = {93E35 (93E20)},
	Mrnumber = {MR1447278 (98c:93120b)},
	Mrreviewer = {G. Yin},
	Number = {3},
	Pages = {355},
	Title = {Correction to: ``{R}ecursive self-tuning control of finite {M}arkov chains''},
	Volume = {24},
	Year = {1997}}

@article{bor96a,
	Author = {Borkar, V. S.},
	Date-Added = {2005-11-29 12:35:43 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Applicationes Mathematicae},
	Issn = {1233-7234},
	Journal = {Appl. Math. (Warsaw)},
	Mrclass = {93E35 (93E20)},
	Mrnumber = {MR1424550 (98c:93120a)},
	Mrreviewer = {G. Yin},
	Number = {2},
	Pages = {169--188},
	Title = {Recursive self-tuning control of finite {M}arkov chains},
	Volume = {24},
	Year = {1996}}

@article{jaajorsin94a,
	Author = {Jaakola, T. and Jordan, M.I. and Singh, S.P},
	Date-Added = {2005-11-29 12:32:11 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Neural Computation},
	Pages = {1185-1201},
	Title = {On the convergence of stochastic iterative dynamic programming algorithms},
	Volume = {6},
	Year = {1994}}

@article{tsi94a,
	Author = {Tsitsiklis, J.N.},
	Date-Added = {2005-11-29 12:30:39 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Machine Learning},
	Pages = {185--202},
	Title = {Asynchronous stochastic approximation and {$Q$}-learning},
	Volume = {16},
	Year = {1994}}

@article{bor98a,
	Author = {Borkar, V. S.},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {62L20 (93E25)},
	Mrnumber = {MR1613869 (99e:62140)},
	Mrreviewer = {Kurt Marti},
	Number = {3},
	Pages = {840--851 (electronic)},
	Title = {Asynchronous stochastic approximations},
	Volume = {36},
	Year = {1998}}

@article{abbberbor01a,
	Author = {Abounadi, J. and Bertsekas, D. and Borkar, V. S.},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {90C40 (93E20)},
	Mrnumber = {MR1871450 (2002h:90109)},
	Mrreviewer = {Mamoru Ohashi},
	Number = {3},
	Pages = {681--698 (electronic)},
	Title = {Learning algorithms for {M}arkov decision processes with average cost},
	Volume = {40},
	Year = {2001}}

@book{benmetpri90,
	Address = {Berlin},
	Author = {Benveniste, A. and M\'etivier, M. and Priouret, P.},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {3-540-52894-6},
	Mrclass = {62L20 (60G35 93E35)},
	Mrnumber = {MR1082341 (92h:62137)},
	Mrreviewer = {G. Pflug},
	Note = {Translated from the French by Stephen S. Wilson},
	Pages = {xii+365},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Adaptive algorithms and stochastic approximations},
	Volume = {22},
	Year = {1990}}

@article{bor97a,
	Author = {Borkar, V. S.},
	Coden = {SCLEDC},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Systems \& Control Letters},
	Issn = {0167-6911},
	Journal = SCL,
	Mrclass = {62L20 (65L20 93E10)},
	Mrnumber = {MR1432654 (97j:62117)},
	Mrreviewer = {G. Yin},
	Number = {5},
	Pages = {291--294},
	Title = {Stochastic approximation with two time scales},
	Volume = {29},
	Year = {1997}}

@article{borsou97a,
	Author = {Borkar, V. S. and Soumyanath, K.},
	Coden = {ITCAEX},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications},
	Issn = {1057-7122},
	Journal = {IEEE Trans. Circuits Systems I Fund. Theory Appl.},
	Mrclass = {65H10},
	Mrnumber = {MR1450259 (98f:65056)},
	Mrreviewer = {E. Kaucher},
	Number = {4},
	Pages = {351--355},
	Title = {An analog scheme for fixed point computation. {I}. {T}heory},
	Volume = {44},
	Year = {1997}}

@article{konbor97a,
	Author = {Konda, V. R. and Borkar, V. S.},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Issn = {0363-0129},
	Journal = SICON,
	Mrclass = {90C40 (68T05)},
	Mrnumber = {MR1740605 (2000k:90073)},
	Mrreviewer = {L. C. Thomas},
	Number = {1},
	Pages = {94--123 (electronic)},
	Title = {Actor-critic-type learning algorithms for {M}arkov decision processes},
	Volume = {38},
	Year = {1999}}

@book{kusyin97,
	Address = {New York},
	Author = {Kushner, H. J. and Yin, G. G.},
	Date-Added = {2005-11-29 12:29:34 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-387-94916-X},
	Mrclass = {62L20 (93E23)},
	Mrnumber = {MR1453116 (98h:62125)},
	Mrreviewer = {M. Bena{\"{\i}}m},
	Pages = {xxii+417},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Stochastic approximation algorithms and applications},
	Volume = {35},
	Year = {1997}}

@book{was69a,
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	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {62.45},
	Mrnumber = {MR0247712 (40 \#975)},
	Pages = {x+202},
	Publisher = {Cambridge University Press},
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	Title = {Stochastic approximation},
	Year = {1969}}

@book{var84a,
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	Author = {Varadhan, S.R.S.},
	Date-Added = {2005-11-07 15:43:56 -0600},
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	Publisher = {Society for Industrial and Applied Mathematics (SIAM)},
	Title = {Large Deviations and Applications},
	Year = {1984}}

@article{csi84,
	Author = {Csisz{\'a}r, I.},
	Date-Added = {2005-11-07 15:39:10 -0600},
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	Journal = ANNP,
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@article{csi98,
	Author = {Csisz{\'a}r, I.},
	Date-Added = {2005-11-07 15:39:10 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TIT,
	Note = {Information theory: 1948--1998},
	Number = {6},
	Pages = {2505-2523},
	Title = {The method of types},
	Volume = {44},
	Year = {1998}}

@book{csibook,
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	Author = {Csisz{\'{a}}r, I. and K{\"{o}}rner, J.},
	Date-Added = {2005-11-07 15:39:10 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Academic Press},
	Title = {Information Theory: Coding Theorems for Discrete Memoryless Systems},
	Year = {1981}}

@article{csi75,
	Author = {Csisz{\'{a}}r, I.},
	Date-Added = {2005-11-07 15:38:09 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNP,
	Pages = {146-158},
	Title = {${I}$-divergence geometry of probability distributions and minimization problems},
	Volume = {3},
	Year = {1975}}

@article{dek87,
	Author = {Dekker, R.},
	Date-Added = {2005-11-06 14:38:51 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Communications in Statistics. Stochastic Models},
	Journal = {Comm. Statist. Stochastic Models},
	Number = {3},
	Pages = {357--368},
	Title = {Counterexamples for compact action {M}arkov decision chains with average reward criteria},
	Volume = {3},
	Year = {1987}}

@book{ros92,
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	Author = {Ross, S. M.},
	Date-Added = {2005-11-06 14:37:49 -0600},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Reprint of the 1970 original},
	Pages = {viii+198},
	Publisher = {Dover Publications Inc.},
	Title = {Applied probability models with optimization applications},
	Year = {1992}}

@book{faymalmen95a,
	Address = {Cambridge},
	Author = {Fayolle, G. and Malyshev, V. A. and Men{\cprime}shikov, M. V.},
	Date-Added = {2005-09-21 08:25:44 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Cambridge University Press},
	Title = {Topics in the constructive theory of countable {M}arkov chains},
	Year = {1995}}

@book{hor77,
	Address = {Amsterdam},
	Author = {Hordijk, A.},
	Date-Added = {2005-09-16 16:17:06 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Mathematical Centre Tracts 51, Mathematisch Centrum},
	Title = {Dynamic Programming and {Markov} Potential Theory, Second Edition},
	Year = {1977}}

@incollection{horkal78,
	Author = {Hordijk, A. and Kallenberg, L. C. M.},
	Booktitle = {Second Symposium on Operations Research, Teil 1, Aachen 1977 (Rheinisch-Westf{\"a}lische Tech. Hochsch. Aachen, Aachen, 1977), Teil 1},
	Date-Added = {2005-09-16 16:08:49 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Mrclass = {90C40},
	Mrnumber = {MR508904 (80c:90147)},
	Mrreviewer = {Ulrich Rieder},
	Pages = {400--406},
	Publisher = {Hain},
	Title = {Linear programming and {M}arkov decision processes},
	Year = {1978}}

@article{denfox68,
	Author = {Denardo, E. V. and Fox, B. L.},
	Date-Added = {2005-09-16 16:08:35 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {SIAM Journal on Applied Mathematics},
	Issn = {1095-712X},
	Journal = {SIAM J. Appl. Math.},
	Mrclass = {90.57},
	Mrnumber = {MR0234721 (38 \#3037)},
	Mrreviewer = {M. Iosifescu},
	Pages = {468--487},
	Title = {Multichain {M}arkov renewal programs},
	Volume = {16},
	Year = {1968}}

@article{wu:00,
	Author = {Wu, L.},
	Date-Added = {2005-09-16 16:02:13 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Acta Math. Sin. (Engl. Ser.)},
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	Pages = {369-394},
	Title = {Some notes on large deviations of {M}arkov processes},
	Volume = {16},
	Year = {2000}}

@article{spi91a,
	Author = {Spieksma, F. M.},
	Date-Added = {2005-09-16 11:20:37 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Annals of Operations Research},
	Issn = {0254-5330},
	Journal = AOR,
	Mrclass = {90B22 (60K25)},
	Mrnumber = {MR1105178 (92c:90057)},
	Number = {1-4},
	Pages = {273--295},
	Title = {The existence of sensitive optimal policies in two multi-dimensional queueing models},
	Volume = {28},
	Year = {1991}}

@article{lerlas97a,
	Author = {Hern{\'a}ndez-Lerma, O. and Lasserre, J. B.},
	Coden = {AAMADV},
	Date-Added = {2005-09-16 11:16:24 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications},
	Issn = {0167-8019},
	Journal = {Acta Appl. Math.},
	Mrclass = {93E20 (90C40)},
	Mrnumber = {MR1449437 (98d:93102)},
	Mrreviewer = {O. L. V. Costa},
	Number = {2},
	Pages = {125--154},
	Title = {Policy iteration for average cost {M}arkov control processes on {B}orel spaces},
	Volume = {47},
	Year = {1997}}

@article{ocaler96,
	Author = {Montes-de-Oca, R. and Hern{\'a}ndez-Lerma, O.},
	Date-Added = {2005-09-16 11:16:24 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications},
	Issn = {0167-8019},
	Journal = {Acta Appl. Math.},
	Mrclass = {93E20 (90C40)},
	Mrnumber = {MR1371202 (96j:93073)},
	Mrreviewer = {O. L. V. Costa},
	Number = {2},
	Pages = {203--222},
	Title = {Value iteration in average cost {M}arkov control processes on {B}orel spaces},
	Volume = {42},
	Year = {1996}}

@book{lerlas96a,
	Address = {New York},
	Author = {Hern{\'a}ndez-Lerma, O. and Lasserre, J. B.},
	Date-Added = {2005-09-16 11:16:24 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-387-94579-2},
	Mrclass = {93-02 (49L20 90C40 93E20)},
	Mrnumber = {MR1363487 (96k:93001)},
	Mrreviewer = {V. S. Borkar},
	Note = {Basic optimality criteria},
	Pages = {xiv+216},
	Publisher = {Springer-Verlag},
	Series = {Applications of Mathematics (New York)},
	Title = {Discrete-time {M}arkov control processes},
	Volume = {30},
	Year = {1996}}

@book{lerlas03,
	Address = {Basel},
	Author = {Hern{\'a}ndez-Lerma, O. and Lasserre, J. B.},
	Date-Added = {2005-09-16 11:14:02 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {3-7643-7000-9},
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	Mrnumber = {MR1974383 (2004b:60002)},
	Mrreviewer = {M. Iosifescu},
	Pages = {xvi+205},
	Publisher = {Birkh{\"a}user Verlag},
	Series = {Progress in Mathematics},
	Title = {Markov chains and invariant probabilities},
	Volume = {211},
	Year = {2003}}

@article{horput87,
	Author = {Hordijk, A. and Puterman, M. L.},
	Date-Added = {2005-09-16 11:10:51 -0500},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Operations Research},
	Issn = {0364-765X},
	Journal = MOR,
	Mrclass = {90C40},
	Mrnumber = {MR882848 (88j:90229)},
	Mrreviewer = {Keigo Yamada},
	Number = {1},
	Pages = {163--176},
	Title = {On the convergence of policy iteration in finite state undiscounted {M}arkov decision processes: the unichain case},
	Volume = {12},
	Year = {1987}}

@article{jon04a,
	Abstract = {

This is an excellent expository paper whose main goal is to describe conditions under which the {Central Limit Theorem} holds for certain {Markov} chains. To be precise, let $\bfmX=(X_{n})_{n\nat},\ N=\{0,1,2,\dots\}$, be a Harris ergodic {Markov} chain on a general measurable state space $(X,\bx)$ with invariant probability distribution $\pi$ on $\bx$ with support $X$.

Let $f$ be a real-valued $\bx$-measurable function on $X$. Define $\overline{f}_{n}=n^{-1}\sum_{i=1}^{n}f(X_{i})$, $n\geq1$, and $E_{\pi}f=\int_{X}fd\pi$. If $E_{\pi}\vert f\vert<\infty$, then the ergodic theorem implies that $\overline{f_{n}}\rightarrow E_{\pi}f$ a.s. as $n\rightarrow\infty$. The conditions discussed refer to $X$ and $f$ in order to ensure that $\sqrt{n} (\overline{f}_{n}-E_{\pi}f)\overset d\to\rightarrow N(0,\sigma_{f}^{2})$ as $n\rightarrow\infty$, where $\sigma_{f}^{2}=\colon{\rm var}_{\pi}\{f(X_{0})\}+2\sum_{n\geq1}{\rm cov}_{\pi} \{f(X_{0}),f(X_{n})\}<\infty$. This is done with a view towards {Markov} chain Monte Carlo settings, hence emphasis is on the connections between the drift and the mixing conditions, and their implications. The point is that when $X$ can be simulated, $\overline{f}_{n}$ is a natural estimate of $E_{\pi}f$. Then the validity of a {Central Limit Theorem} allows one to estimate $\sigma _{f}^{2}$ in order to decide whether $\overline{f}_{n}$ is a good estimate of $E_{\pi}f.$

\{Reviewer's remark: Another survey paper on the {Central Limit Theorem} for reversible {Markov} processes, which is not included in the references of the present paper, has been recently published by C. Landim \ref[in From classical to modern probability, 145--205, Birkh{\"a}user, Basel, 2003; MR2045987 (2005b:60055)].\}
Reviewed by M. Iosifescu
},
	Author = {Jones, G. L.},
	Date-Added = {2005-09-15 20:53:35 -0500},
	Date-Modified = {2008-01-02 18:53:38 -0600},
	Fjournal = {Probability Surveys},
	Issn = {1549-5787},
	Journal = {Probab. Surv.},
	Mrclass = {60J05 (60F05)},
	Mrnumber = {MR2068475 (2005j:60137)},
	Mrreviewer = {M. Iosifescu},
	Pages = {299--320 (electronic)},
	Title = {On the {M}arkov chain {Central Limit Theorem}},
	Volume = {1},
	Year = {2004}}

@book{ber03,
	Address = {Cambridge, Mass},
	Author = {Bertsekas, D.P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {{with Angelia Nedic and Asuman E. Ozdaglar}},
	Publisher = {Atena Scientific},
	Title = {Convex Analysis and Optimization},
	Year = {2003}}

@book{bertsi96a,
	Address = {Cambridge, Mass},
	Author = {Bertsekas, D.P. and Tsitsiklis, J. N.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Atena Scientific},
	Title = {Neuro-Dynamic Programming},
	Year = {1996}}

@article{lju77a,
	Author = {Ljung, L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TAC,
	Number = {4},
	Pages = {539--551},
	Title = {On positive real transfer functions and the convergence of some recursive schemes},
	Volume = {AC-22},
	Year = {1977}}

@incollection{ben99a,
	Address = {Berlin},
	Author = {Bena\"im, M.},
	Booktitle = {S\'eminaire de Probabilit\'es, XXXIII},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {1--68},
	Publisher = {Springer},
	Title = {Dynamics of stochastic approximation algorithms},
	Year = {1999}}

@article{kusshw84a,
	Author = {Kushner, H. J. and Shwartz, A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Number = {1},
	Pages = {13--27},
	Title = {An invariant measure approach to the convergence of stochastic approximations with state dependent noise},
	Volume = {22},
	Year = {1984}}

@article{ger91,
	Author = {Gerencs\'er, L{\'a}szl{\'o}},
	Coden = {STOCBS},
	Date-Modified = {2008-01-21 23:12:25 -0500},
	Fjournal = {Stochastics and Stochastics Reports},
	Issn = {1045-1129},
	Journal = {Stochastics Stochastics Rep.},
	Mrclass = {34F05 (34D99 60H10 93E15)},
	Mrnumber = {92i:34077},
	Mrreviewer = {Wolfgang Kliemann},
	Number = {2},
	Pages = {91--107},
	Title = {Almost sure exponential stability of random linear differential equations},
	Volume = {36},
	Year = {1991}}

@article{bezose96,
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	Journal = {Teor. Veroyatnost. i Primenen.},
	Number = {3},
	Pages = {633-639},
	Title = {On the variance of sums for functions of a stationary {M}arkov process},
	Volume = {41},
	Year = {1996}}

@book{basols95,
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	Author = {Ba{\c{s}}ar, T., T. and Olsder, G. J.},
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	Note = {Second Edition},
	Publisher = {Academic Press},
	Title = {{Dynamic Noncooperative Game Theory}},
	Year = {1995}}

@book{bel57,
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	Publisher = {Princeton University Press},
	Title = {{Dynamic Programming}},
	Year = {1957}}

@book{boyvan04a,
	Address = {New York},
	Author = {Boyd, S. and Vandenberghe, L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Edition = {1st},
	Publisher = {Cambridge University Press},
	Title = {Convex Optimization},
	Year = {2004}}

@unpublished{vanboycom04,
	Author = {Vandenberghe, L. and Boyd, S. and Comanor, K.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Submitted to SIAM Review, Problems and Techniques Section, January 2004},
	Title = {Generalized {Chebyshev} bounds via semidefinite programming}}

@article{chiboy04,
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	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {IEEE Transactions on Information Theory},
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	Pages = {245-258},
	Title = {Geometric programming duals of channel capacity and rate distortion},
	Volume = {50},
	Year = {2004}}

@book{shwwei95,
	Address = {London},
	Author = {Shwartz, A. and Weiss, A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-412-06311-5},
	Mrclass = {60F10 (60K25 60K30 68M20 90B22)},
	Mrnumber = {MR1335456 (96i:60029)},
	Mrreviewer = {J. D. Biggins},
	Note = {Queues, communications, and computing, With an appendix by Robert J. Vanderbei},
	Pages = {x+556},
	Publisher = {Chapman \& Hall},
	Series = {Stochastic Modeling Series},
	Title = {Large deviations for performance analysis},
	Year = {1995}}

@book{sabsim94a,
	Address = {P.O. Box 346, 3700 AH Zeist, The Netherlands.},
	Author = {Sabelfeld, K.K. and Simonov, N. A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {VSP Intl.\ Science Publishers},
	Title = {Random Walks on Boundary for Solving PDEs},
	Volume = {11},
	Year = {1994}}

@book{gla03,
	Address = {NY, NY},
	Author = {Glasserman, P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Springer Verlag},
	Series = {Applications of Mathematics},
	Title = {Monte Carlo Methods in Financial Engineering},
	Volume = {53},
	Year = {2003}}

@book{bin86a,
	Address = {NY, NY},
	Author = {Binder, K.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Springer-Verlag},
	Title = {Monte Carlo Methods in Statistical Physics},
	Year = {1986}}

@book{ben82a,
	Address = {Amsterdam},
	Author = {Bensoussan, A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {xv+410},
	Publisher = {North-Holland Publishing Co.},
	Series = {Studies in Mathematics and its Applications},
	Title = {Stochastic control by functional analysis methods},
	Volume = {11},
	Year = {1982}}

@book{benlio82a,
	Address = {Paris},
	Author = {Bensoussan, A. and Lions, J.-L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {xv+596},
	Publisher = {Gauthier-Villars},
	Series = {M\'ethodes Math\'ematiques de l'Informatique [Mathematical Methods of Information Science]},
	Title = {Contr\^ole impulsionnel et in\'equations quasi variationnelles (Impulse control and quasivariational inequalities)},
	Volume = {11},
	Year = {1982}}

@article{bla74a,
	Author = {Blahut, R. E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {IEEE Trans. Information Theory},
	Pages = {405--417},
	Title = {Hypothesis testing and information theory},
	Volume = {IT-20},
	Year = {1974}}

@book{bor89a,
	Address = {Harlow},
	Author = {Borkar, V. S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Isbn = {0-582-03540-6},
	Mrclass = {93E20 (49A60 49C10 60H10 60J60 93-02)},
	Mrnumber = {90h:93115},
	Mrreviewer = {Anatoli\u{\i} B. Juditsky},
	Pages = {vi+196},
	Publisher = {Longman Scientific \& Technical},
	Series = {Pitman Research Notes in Mat hematics Series},
	Title = {Optimal control of diffusion processes},
	Volume = {203},
	Year = {1989}}

@article{borgho92a,
	Author = {Borkar, V. S. and Ghosh, M. K.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Mathematics of Control, Signals, and Systems},
	Journal = MCSS,
	Number = {4},
	Pages = {453},
	Title = {Correction: ``{E}rgodic and adaptive control of nearest-neighbor motions'' [{M}ath.\ {C}ontrol {S}ignals {S}ystems {\bf 4} (1991), no.\ 1, 81--98; {MR} 92e:93026]},
	Volume = {5},
	Year = {1992}}

@article{borgho92b,
	Author = {Borkar, V. S. and Gho sh, M. K.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Journal of Optimization Th eory and Applications},
	Journal = {J. Optim. Theory Appl.},
	Number = {2},
	Pages = {359--385},
	Title = {Stochastic differential games: occupation measure based approach},
	Volume = {73},
	Year = {1992}}

@article{tebvaj93,
	Author = {Teboulle, Marc and Vajda, Igor},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {IEEE Transactions on Information Theory},
	Number = {1},
	Pages = {297-},
	Title = {Convergence of best $\varphi$-entropy estimates.},
	Volume = {39},
	Year = {1993}}

@article{nadzog03,
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	Journal = {Inf. Sci.},
	Number = {1-2},
	Pages = {119--138},
	Title = {Formulas for Renyi information and related measures for univariate distributions},
	Volume = {155},
	Year = {2003}}

@incollection{borlew93a,
	Address = {Dordrecht},
	Author = {Borwein, J.M. and Lewis, A.S.},
	Booktitle = {Maximum Entropy and Bayesian Methods},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Mohammad-Djafari, A. and Demoment, G.},
	Pages = {39-48},
	Publisher = {Kluwer Academic},
	Title = {A survey of convergence results for maximum entropy},
	Year = {1993}}

@article{borlew91a,
	Author = {Borwein, J. M. and Lewis, A. S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {SIAM J. Optim.},
	Number = {2},
	Pages = {191--205},
	Title = {Convergence of best entropy estimates},
	Volume = {1},
	Year = {1991}}

@article{borlew92b,
	Author = {Borwein, J. M. and Lewis, A. S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Math. Program.},
	Pages = {49-83},
	Title = {Partially finite convex programming, {Part II}: Explicit lattice models.},
	Volume = {57},
	Year = {1992}}

@article{borlew92a,
	Author = {Borwein, Jonathan M. and Lewis, A. S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Math. Program.},
	Pages = {15-48},
	Title = {Partially finite convex programming, {Part I}: Quasi relative interiors and duality theory.},
	Volume = {57},
	Year = {1992}}

@article{bormey02a,
	Author = {Borkar, V. S. and Meyn, S. P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = MOR,
	Number = {1},
	Pages = {192--209},
	Title = {Risk-sensitive optimal control for {M}arkov decision processes with monotone cost},
	Volume = {27},
	Year = {2002}}

@article{bormey00a,
	Author = {Borkar, V. S. and Meyn, S. P.},
	Date-Modified = {2009-09-12 19:53:48 +0300},
	Journal = SICON,
	Note = {(also presented at the {\it IEEE CDC}, December, 1998)},
	Number = {2},
	Pages = {447--469},
	Title = {The {ODE} method for convergence of stochastic approximation and reinforcement learning},
	Volume = {38},
	Year = {2000}}

@article{aldtho93,
	Author = {Aldous, D. J. and Thorisson, H.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SPA,
	Pages = {1--4},
	Title = {Shift-Coupling},
	Volume = {44},
	Year = {1993}}

@article{balmey00a,
	Author = {Balaji, S. and Meyn, S. P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SPA,
	Number = {1},
	Pages = {123--144},
	Title = {Multiplicative ergodicity and large deviations for an irreducible {M}arkov chain},
	Volume = {90},
	Year = {2000}}

@book{hirlem93a,
	Address = {Berlin},
	Author = {Hiriart-Urruty, J.-B. and Lemar{\'e}chal, C.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
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@techreport{liu92,
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@book{karshr88,
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	Booktitle = {Probability, Statistics and Optimization},
	Date-Modified = {2007-07-11 11:01:34 -0400},
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	Pages = {173--183},
	Publisher = {John Wiley and Sons},
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	Year = {1993}}

@article{strtwebro93b,
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@article{strbrotwe93a,
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	Journal = ANNP,
	Pages = {879--880},
	Title = {{Orthogonal measure: An example}},
	Year = {1982}}

@article{mal72,
	Author = {Maly\v{s}hev, V. A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Soviet Math. Dokl.},
	Pages = {136--139},
	Title = {Classification of two-dimensional positive random walks and almost linear semi-Martingales},
	Volume = {13},
	Year = {1972}}

@article{malmen79,
	Author = {Maly{\v{s}}ev, V. A. and Men{\cprime}{\v{s}}ikov, M. V.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Fjournal = {Trudy Moskovskogo Matematicheskogo Obshchestva},
	Journal = {Trudy Moskov. Mat. Obshch.},
	Note = {\textit{Trans. Moscow Math. Soc.}, pp. 1-48, 1981.},
	Pages = {3--48, 235},
	Title = {Ergodicity, continuity and analyticity of countable {M}arkov chains},
	Volume = {39},
	Year = {1979}}

@article{mar55,
	Author = {Marschak, J.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = MS,
	Pages = {127--137},
	Title = {Elements for a theory of teams},
	Volume = {1},
	Year = {1955}}

@article{mar59,
	Author = {Marschak, T.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Econometrica},
	Pages = {399--430},
	Title = {Centralization and decentralization in economic organizations},
	Volume = {27},
	Year = {1959}}

@article{mar06,
	Author = {Markov, A. A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Izv. Fiz.-Matem. Obsch. Kazan Univ. (2nd Ser)},
	Pages = {135--156},
	Title = {Extension of the law of large numbers to dependent quantities [in {R}ussian]},
	Volume = {15},
	Year = {1906}}

@article{mar73,
	Author = {Marlin, P. G.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Operations Res.},
	Pages = {617--622},
	Title = {On the ergodic theory of {Markov} chains},
	Volume = {21},
	Year = {1973}}

@book{mar76a,
	Address = {Oxford, England},
	Author = {Margaria, R.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Oxford University Press},
	Title = {{Biomechanics and Energetics of Muscular Exercise}},
	Year = {1976}}

@article{marbit86,
	Author = {Mareels, {I. M. Y.} and Bitmead, R. R.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AUTOM,
	Pages = {641--655},
	Title = {Non-linear Dynamics in Adaptive Control: Chaotic and Periodic Stabilization},
	Volume = {22},
	Year = {1986}}

@article{marbit88,
	Author = {Mareels, {I. M. Y.} and Bitmead, R. R.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = CAS,
	Pages = {835--841},
	Title = {Bifurcation effects in robust adaptive control},
	Volume = {35},
	Year = {1988}}

@article{mau58,
	Author = {Mauldon, J. G.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Proc. Cambridge Phil. Soc.},
	Pages = {825--835},
	Title = {On non-dissipative {Markov} chains},
	Volume = {53},
	Year = {1958}}

@article{may63,
	Author = {Mayne, D. Q.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {J. Electron. Contr.},
	Pages = {101},
	Title = {Optimal nonstationary estimation of the parameters of a linear system with {Gaussian} inputs},
	Volume = {14},
	Year = {1963}}

@article{men74,
	Author = {Men'\v{s}ikov, M. V.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Soviet Math. Dokl.},
	Pages = {1118--1121},
	Title = {Ergodicity and transience conditions for random walks in the positive octant of space},
	Volume = {15},
	Year = {1974}}

@article{mersamzam78,
	Author = {Mertens, J.-F. and Samuel-Cahn, E. and Zamir, S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = JAP,
	Pages = {848--851},
	Title = {Necessary and sufficient conditions for recurrence and transience of {Markov} chains, in terms of inequalities},
	Volume = {15},
	Year = {1978}}

@article{met69,
	Author = {Metivier, M.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNMS,
	Pages = {74--96},
	Title = {Existence of an invariant measure and an {O}rnstein's ergodic theorem},
	Volume = {40},
	Year = {1969}}

@article{mey62,
	Author = {Meyer, P.- A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Ann. Inst. Fourier, Grenoble},
	Pages = {125--230},
	Title = {Fonctionelles multiplicatives et additives de {Markov}},
	Volume = {12},
	Year = {1962}}

@phdthesis{mey87,
	Address = {Montr\'{e}al, Qu\'{e}bec, Canada},
	Author = {Meyn, S. P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Department of Electrical Engineering},
	School = {McGill University},
	Title = {Asymptotic Behavior of Stochastic Systems Processing {Markovian} Realizations},
	Year = {1987}}

@inproceedings{mey88a,
	Address = {Beijing, China},
	Author = {Meyn, S. P.},
	Booktitle = {Proceedings of the 1988 {IFAC} Symposium on Identification and System Parameter Estimation},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {247--252},
	Title = {The structural robustness of stochastic systems},
	Year = {1988}}

@inproceedings{mey88b,
	Address = {Austin, Texas},
	Author = {Meyn, S. P.},
	Booktitle = CDC27,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Title = {On the stability and structural robustness of nonlinear stochastic systems},
	Year = {1988}}

@article{mey89a,
	Author = {Meyn, S. P.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Pages = {1409--1439},
	Title = {Ergodic theorems for discrete time stochastic systems using a stochastic {{Lyapunov}} function},
	Volume = {27},
	Year = {1989}}

@inproceedings{meybro90a,
	Address = {Honolulu, HI},
	Author = {Meyn, S. P. and Brown, L.},
	Booktitle = CDC90,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {1432--1437},
	Title = {Adaptive control using a {Kalman} filter based estimation algorithm},
	Year = {1990}}

@incollection{meybro91,
	Address = {Lawrence, KS},
	Author = {Meyn, S. P. and Brown, L. J.},
	Booktitle = {Workshop on Stochastic Theory-Adaptive Control},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {{}},
	Publisher = {University of Kansas},
	Title = {Model Reference Adaptive Control for Linear Stochastic Systems},
	Year = {1991}}

@article{meybro93,
	Author = {Meyn, S. P. and Brown, L. J.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TAC,
	Pages = {1738--1753},
	Title = {Model Reference Adaptive Control of Time Varying and Stochastic Systems},
	Volume = {38},
	Year = {1993}}

@inproceedings{bromey95,
	Address = {New Orleans, LA},
	Author = {Brown, L. and Meyn, S. P.},
	Booktitle = CDC95,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Title = {Adaptive Dead Time Compenastion with Application to Robotic Welding},
	Year = {1995}}

@article{meycai85,
	Author = {Meyn, S. P. and Caines, P. E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Systems and Control Letters},
	Pages = {235--238},
	Title = {The Zero Divisor Problem of Multivariable Stochastic Adaptive Control},
	Volume = {6},
	Year = {1985}}

@article{meycai87a,
	Author = {Meyn, S. P. and Caines, P. E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TAC,
	Pages = {220--226},
	Title = {A new approach to stochastic adaptive control},
	Volume = {AC-32},
	Year = {1987}}

@book{meycai87b,
	Address = {Phoenix, AZ},
	Author = {Meyn, S. P. and Caines, P. E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Organization = {University of Arizona},
	Publisher = {University of Arizona},
	Title = {{Ergodicity and periodicity in stochastic systems}},
	Year = {1987}}

@inproceedings{meycai87c,
	Address = {Los Angeles, CA},
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = CDC87,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {1647--1652},
	Title = {Ergodicity and periodicity in Stochastic Systems},
	Year = {1987}}

@conference{meycai87d,
	Address = {Baltimore, MD},
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = {Conference on Information Sciences and Systems},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Organization = {Johns Hopkins University},
	Title = {{Markov} processes, ergodicity, and stochastic system theory},
	Year = {1987}}

@inproceedings{meycai87e,
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = {Proceedings of the 1988 {IFAC} Symposium on Identification and System Parameter Estimation},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {140--148},
	Title = {On the steady state behavior of stochastic systems with applications to adaptive control},
	Year = {1987}}

@inproceedings{meycai87f,
	Address = {Dubrovnik, Yugoslavia},
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = {Proceedings of the 2nd pre-{IFAC} Congress get-together; current trends in adaptive control},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Title = {On the steady state behavior of stochastic systems with applications to adaptive control},
	Year = {1987}}

@inproceedings{meycai89a,
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = {{IFAC} Adaptive Symposium, Glasgow},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Title = {Mean exit times and rates of convergence for stochastic systems with applications to adaptive control},
	Year = {1989}}

@inproceedings{meycai89b,
	Address = {Berlin},
	Author = {Meyn, S. P. and Caines, P. E.},
	Booktitle = {Stochastic Differential Systems. Proceedings of the 4th Bad Honnef Conference},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {235--257},
	Publisher = {Springer-Verlag},
	Title = {Stochastic controllability and stochastic {{Lyapunov}} functions with applications to adaptive and nonlinear systems},
	Year = {1989}}

@article{meycai91,
	Author = {Meyn, S. P. and Caines, P. E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = SICON,
	Pages = {535--561},
	Title = {Asymptotic Behavior of Stochastic Systems Processing {Markovian} Realizations},
	Volume = {29},
	Year = {1991}}

@inproceedings{meyfra90a,
	Address = {Honolulu, HI},
	Author = {Meyn, S. P. and Frater, M.},
	Booktitle = CDC90,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Also under revision {IEEE} Transactions on Information Theory},
	Pages = {876--880},
	Title = {Recurrence times of buffer overflows in {Jackson} Networks},
	Year = {1990}}

@inproceedings{meyguo89,
	Address = {Tampa, FL},
	Author = {Meyn, S. P. and Guo, L.},
	Booktitle = CDC89,
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Pages = {2108--2113},
	Title = {Stability, convergence, and performance of an adaptive control algorithm applied to a randomly varying system},
	Year = {1989}}

@inproceedings{meyguo90c,
	Address = {Tallinn, Estonia, USSR},
	Author = {Meyn, S. P. and Guo, L.},
	Booktitle = {Proceedings of the 11th {IFAC} World Congress},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Editor = {Utkin, V. and Jaaksoo, O.},
	Pages = {198--202},
	Title = {Adaptive Control of Time Varying stochastic Systems},
	Volume = {3},
	Year = {1990}}

@article{meyguo92b,
	Author = {Meyn, S. P. and Guo, L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = TAC,
	Pages = {535--540},
	Title = {Stability, convergence, and performance of an adaptive control algorithm applied to a randomly varying system},
	Volume = {AC-37},
	Year = {1992}}

@misc{meytwe90,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Howpublished = {Presented at {SIAM} Conference on Applied Probability in Science and Engineering},
	Note = {Clarion Hotel, New Orleans, LA},
	Title = {Stability Conditions for Continuous time processes},
	Year = {1990}}

@article{meytwe94a,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNAP,
	Pages = {149--168},
	Title = {State-Dependent Criteria for Convergence of {Markov} Chains},
	Volume = {4},
	Year = {1994}}

@inproceedings{meytwe94c,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Booktitle = {Proceedings of the Workshop on Stochastic Stability and Stochastic Stabilization, {Metz, France, June 1993}},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Title = {A Survey of {Foster-{Lyapunov}} Techniques for General State Space {Markov} Processes},
	Year = {1994}}

@article{meytwe94b,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNAP,
	Pages = {981-1011},
	Title = {Computable bounds for convergence rates of {Markov chains}},
	Volume = {4},
	Year = {1994}}

@article{meytwe92a,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AAP,
	Pages = {542-574},
	Title = {Stability of {Markovian} processes {I}: {D}iscrete time chains},
	Volume = {24},
	Year = {1992}}

@article{meytwe93a,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AAP,
	Pages = {487--517},
	Title = {Stability of {Markovian} processes {II}: Continuous Time Processes and Sampled Chains},
	Volume = {25},
	Year = {1993}}

@article{meytwe93b,
	Author = {Meyn, S. P. and Tweedie, R. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AAP,
	Pages = {518--548},
	Title = {Stability of {Markovian} processes {III}: {Foster}-{{Lyapunov}} Criteria for Continuous Time Processes},
	Volume = {25},
	Year = {1993}}

@article{mil66,
	Author = {Miller, H. D.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ZW,
	Pages = {354-373},
	Title = {Geometric ergodicity in a class of denumerable {Markov} chains},
	Volume = {4},
	Year = {1966}}

@techreport{mit91,
	Address = {Stony Brook, NY},
	Author = {Mittnik, S.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Institution = {State University of New York at Stony Brook},
	Number = {WP-91-06},
	Title = {Nonlinear Time Series Analysis with Generalized Autoregressions: {A} State Space Approach},
	Type = {Working Paper},
	Year = {1991}}

@article{mok87a,
	Author = {Mokkadem, A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = JTSA,
	Pages = {195--204},
	Title = {Sur un mod\'{e}le autor\'{e}gressif non lin\'{e}air: ergodicit\'{e} et ergodicit\'{e} g\'{e}om\'{e}trique},
	Volume = {8},
	Year = {1987}}

@phdthesis{mok87b,
	Address = {Centre d'Orsay},
	Author = {Mokkadem, A.},
	Date-Modified = {2007-12-10 06:49:31 -0600},
	School = {Universit\'{e} Paris Sud},
	Title = {Criteres de melange pour des processus stationnaires. Estimation sous des hypotheses de melange. Entropie de processus lineaires.},
	Year = {1987}}

@article{mok88,
	Author = {Mokkadem, A.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {in new trends on nonlinear control theory},
	Note = {Lecture notes in control and information sciences},
	Pages = {404--413},
	Title = {Ergodicit\'{e} des syst\'{e}mes stochastiques polynomiaux en temps discret.},
	Volume = {122},
	Year = {1988}}

@inproceedings{mok89,
	Author = {Mokkadem, A.},
	Booktitle = {{IFAC} symposium on nonlinear systems designs},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Capri},
	Title = {On the controllability of nonlinear discrete time systems},
	Year = {1989}}

@article{mor53,
	Author = {Moran, {P. A. P.}},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Aust. J. Zool.},
	Pages = {163--173},
	Title = {The Statistical Analysis of the {Canadian} lynx cycle {I:} Structure and Prediction},
	Volume = {1},
	Year = {1953}}

@book{mor59,
	Address = {London},
	Author = {Moran, {P. A. P.}},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Publisher = {Methuen},
	Title = {{The Theory of Storage}},
	Year = {1959}}

@article{mou57,
	Author = {Moustafa, M. D.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Proc. Koninkl. Ned. Akad. Wetensch.},
	Pages = {112-118},
	Title = {Input-output {M}arkov processes},
	Volume = {A60},
	Year = {1957}}

@article{neynum87a,
	Author = {Ney, P. and Nummelin, E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNP,
	Number = {2},
	Pages = {561-592},
	Title = {Markov additive processes. {I}. {Eigenvalue} properties and limit theorems},
	Volume = {15},
	Year = {1987}}

@article{neynum87b,
	Author = {Ney, P. and Nummelin, E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = ANNP,
	Number = {2},
	Pages = {593-609},
	Title = {Markov additive processes {II}. {Large} deviations},
	Volume = {15},
	Year = {1987}}

@article{nel58,
	Abstract = { Let $X$ be a locally compact Hausdorff space, let $C$ be the space of continuous functions on $X$, vanishing at $\infty$, and let $B$ be a linear space (with supremum norm) of bounded continuous functions on $X$, containing $C$. Let $P$ be a linear transformation of $B$ into itself, taking positive $(\geq 0)$ functions into positive functions, of norm $\leq 1$, with $P1=1$ if $X$ is compact, and suppose that for every positive $f$ in $B$ and every $x$ in $X$, $\sup_n\,(P^nf)(x)>0$. An existence theorem for linear functionals is proved implying that there is a regular measure $m$ on $X$ such that $mU>0$ if $U$ is open and not empty, and that $\int Pf\,dm\leq\int f\,dm$ if $f$ is positive and has compact support. A corresponding result for semigroups of transformations on $B$ is also obtained.

Now suppose that $X$ is any measurable space with the same structure as a Borel linear set. In the following, all measures are to be understood to be totally sigma finite. Let $p$ be a substochastic transition function: $p(x,\cdot )$ is a measure for each $x$; $p(\cdot,E)$ is measurable for each $E$; $p\leq 1$. If the integrals make sense, define $$ (Pf)(x)=\int f(y)p(x,dy),\quad(P^*\mu )(E)=\int p(x,E)d\mu (x). $$ If $P^*\mu \leq \mu $, $\mu $ is called `subinvariant', `invariant' if there is equality. If $p$ is substochastic, and if $m$ is a subinvariant measure, it is shown that $P$ is well-defined on $L^\alpha(m)$, and that $P^*f$ can be defined for $f$ in $L^1$ (and by extension to $L^\alpha$) as the Radon-Nikodym derivative with respect to $m$ of $P^*\mu $, where $d\mu =fdm$. There is then a simple adjointness relationship between $P$ on $L^\alpha$ and $P^*$ on $L^\beta$, where $1/\alpha+1/\beta=1$. Moreover $P^*f$ is itself determined by a substochastic transition function $p^*$. If $$ \nu_x(E)=\sum_1^\infty2^{-n}p^n(x,E), $$ where $p^n$ is the $n$th iterate of the kernel $p$, and if $(*)$$\nu_x$ has the same null sets for every $x,p$ and $p^*$ are determined by transition densities which are a.e. transposes of each other.

Results on invariant measures are obtained which yield the following, with the help of a theorem of Harris [Proc. Third Berkeley Symposium Math. Statist. Probability, 1954--1955, vol. II, pp. 113--124, Univ. of California Press, Berkeley, 1956; MR0084889 (18,941d)]. If $p$ is substochastic, if $(*)$ is satisfied, if there is a point $x_0$ in $X$ with $\sum_1^\infty p^n(x_0,E)=\infty$ whenever $\nu_x(E)>0$, then there is an invariant measure $m$ with the same null sets as $\nu_x$, and such that every subinvariant measure is a multiple of $m$.

If $X$ is a differentiable manifold, and if there is a semigroup with infinitesimal generator a second order elliptic differential operator acting on functions on $X$, it is shown as an application that there is a unique invariant probability measure, and the adjoint semigroup is identified.},
	Author = {Nelson, E.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = DMJ,
	Pages = {671-690},
	Title = {The adjoint {Markoff} process},
	Volume = {25},
	Year = {1958}}

@article{neu67,
	Author = {Neuts, M. F.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Sankhy\={a} Ser. A},
	Pages = {259--264},
	Title = {Two {Markov} chains arising from examples of queues with state dependent service times},
	Volume = {297},
	Year = {1967}}

@article{neu78,
	Author = {Neuts, M. F.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = AAP,
	Pages = {185--212},
	Title = {{Markov} chains with applications in queueing theory, which have a matrix- geometric invariant probability vector},
	Volume = {10},
	Year = {1978}}

@article{neuteu69,
	Author = {Neuts, M. F. and Teugels, J. L.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {SIAM J. Appl. Math.},
	Pages = {921--929},
	Title = {Exponential ergodicity of the {M/G/1} queue},
	Volume = {17},
	Year = {1969}}

@book{nevhas73a,
	Address = {Providence, R. I.},
	Author = {Nevel{\cprime}son, M. B. and Has{\cprime}minski{\u\i}, R. Z.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Note = {Translated from the Russian by the Israel Program for Scientific Translations, Translations of Mathematical Monographs, Vol. 47},
	Pages = {iv+244},
	Publisher = {American Mathematical Society},
	Title = {Stochastic approximation and recursive estimation},
	Year = {1973}}

@article{nev61a,
	Author = {Neveu, J.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Abh. Math. Sem. Univ. Hamburg},
	Pages = {36--61},
	Title = {Une g\'{e}n\'{e}ralisation des processus \`{a} accroisements croissants ind\'{e}pendants},
	Volume = {25},
	Year = {1961}}

@inproceedings{nev61b,
	Address = {Berkeley, CA},
	Author = {Neveu, J.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
	Journal = {Proc. 4th Berkeley Symposium of Math. Statist. and Probability},
	Pages = {347--391},
	Publisher = {University of California Press},
	Title = {Lattice methods and sub-{M}arkovian processes},
	Volume = {{II}},
	Year = {1961}}

@article{nev64,
	Author = {Neveu, J.},
	Date-Modified = {2007-07-11 11:01:34 -0400},
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@article{twe74a,
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@article{twe74b,
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@article{twe74c,
	Abstract = { The results here are based on the "$R$-theory" of {Markov} chains on a general state space, which was developed by the author in two papers [Ann. Probability 2 (1974), 840--864; MR0368151 (51 \#4393); ibid. 2 (1974), 865--878; MR0368152 (51 \#4394)]. They generalize from countable to general state space (to Harris chains) the natural set of results concerning the three different types of quasi-stationary distributions (for the countable case see E. Seneta and D. Vere-Jones [J. Appl. Probability 3 (1966), 403--434; MR0207047 (34 \#6863)]).},
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@article{twe75a,
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