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© 2003

Markov Chains and Invariant Probabilities

Book

Part of the Progress in Mathematics book series (PM, volume 211)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Preliminaries

    1. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 1-18
  3. Markov Chains and Ergodicity

    1. Front Matter
      Pages 19-19
    2. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 21-39
    3. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 41-46
    4. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 47-61
    5. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 63-82
    6. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 83-92
  4. Further Ergodicity Properties

    1. Front Matter
      Pages 93-93
    2. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 95-102
    3. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 103-120
    4. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 121-131
  5. Existence and Approximation of Invariant Probability Measures

    1. Front Matter
      Pages 133-133
    2. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 135-155
    3. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 157-174
    4. Onésimo Herná-Lerma, Jean Bernard Lasserre
      Pages 175-191
  6. Back Matter
    Pages 193-208

About this book

Introduction

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.

Keywords

Markov chain ergodicity mathematical methods in physics probability measure probability theory

Authors and affiliations

  1. 1.Departamento de MatemáticasCINVESTAV-IPNMéxicoMéxico
  2. 2.LAAS-CNRSFrance

Bibliographic information

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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