Progress in Mathematics

By: Siegfried Wichmann, Onesimo Hernandez-Lerma, Jean Bernard Lasserre

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Hardcover | 24 February 2003

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This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

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"It should be stressed that an important part of the results presented is due to the authors. . . . In the reviewer's opinion, this is an elegant and most welcome addition to the rich literature of Markov processes."

--MathSciNet

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Non-Fiction Mathematics Applied Mathematics Stochastics Probability & Statistics Business & Management Operational Research Science Physics Mathematical Physics Management & Management Techniques

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Published: 23rd October 2012

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Acknowledgements
Preface
Abbreviations and List of Symbols
Preliminaries	p. 1
Markov Chains and Ergodicity	p. 19
Markov Chains and Ergodic Theorems	p. 21
Countable Markov Chains	p. 41
Harris Markov Chains	p. 47
Markov Chains in Metric Spaces	p. 63
Classification of Markov Chains via Occupation Measures	p. 83
Further Ergodicity Properties	p. 93
Feller Markov Chains	p. 95
The Poisson Equation	p. 103
Strong and Uniform Ergodicity	p. 121
Existence and Approximation of Invariant Probability Measures	p. 133
Existence of Invariant Probability Measures	p. 135
Existence and Uniqueness of Fixed Points for Markov Operators	p. 157
Approximation Procedures for Invariant Probability Measures	p. 175
Bibliography	p. 193
Index	p. 203
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

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Hardcover

Industry Reviews

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You Can Find This Book In

Other Editions and Formats

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