Markov Chains and Invariant Probabilities
By: by Onésimo Hernández-Lerma, Jean Bernard Lasserre
Contributors: Lasserre, Jean Bernard
Series: Progress in Mathematics -- 211; Progress in Mathematics -- 211
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2003
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 206
ISBN-13: 9783034894081; 9783034880244
Subjects: Mathematics; Distribution (Probability theory); Mathematical physics
Description: This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure. The main objective is to give a systematic, self-contained presentation on some key issues about the ergodic behavior of that class of Markov chains. These issues include, in particular, the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space. Some of the results presented appear for the first time in book form. A distinguishing feature of the book is the emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces. The intended audience are graduate students and researchers in theoretical and applied probability, operations research, engineering and economics.
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Table of contents: title: Preliminaries; title: Markov Chains and Ergodic Theorems; title: Countable Markov Chains; title: Harris Markov Chains; title: Markov Chains in Metric Spaces; title: Classification of Markov Chains via Occupation Measures; title: Feller Markov Chains; title: The Poisson Equation; title: Strong and Uniform Ergodicity; title: Existence of Invariant Probability Measures; title: Existence and Uniqueness of Fixed Points for Markov Operators; title: Approximation Procedures for Invariant Probability Measures.