Overview
- Some of the results presented appear for the first time in book form
- Emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces
Part of the book series: Progress in Mathematics (PM, volume 211)
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About this book
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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Table of contents (12 chapters)
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Front Matter
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Preliminaries
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Markov Chains and Ergodicity
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Front Matter
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Further Ergodicity Properties
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Front Matter
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Existence and Approximation of Invariant Probability Measures
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Front Matter
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Back Matter
Reviews
"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
Authors and Affiliations
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Bibliographic Information
Book Title: Markov Chains and Invariant Probabilities
Authors: Onésimo Hernández-Lerma, Jean Bernard Lasserre
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-8024-4
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Verlag 2003
Hardcover ISBN: 978-3-7643-7000-8Published: 24 February 2003
Softcover ISBN: 978-3-0348-9408-1Published: 23 October 2012
eBook ISBN: 978-3-0348-8024-4Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XVI, 208
Topics: Probability Theory and Stochastic Processes, Operations Research, Management Science, Mathematical Methods in Physics