Markov Chains and Invariant Probabilities

Onesimo Hernandez-Lerma and Jean B. Lasserre,

Birkhauser-Verlag, Basel, 2003.  ISBN 3-7643-7000-9

PREFACE

CHAPTER 1. Preliminaries

  • 1.1. Introduction
  • 1.2. Measures and functions
  • 1.3. Weak topologies
  • 1.4. Convergence of measures
  • 1.5 Complements

    •  

    PART I. MCs and Ergodicity

    CHAPTER 2. MCs and ergodic theorems

  • 2.1. Introduction
  • 2.2. Basic notation and definitions
  • 2.3. Ergodic theorems
  • 2.4. The ergodicity property
  • 2.5. Pathwise results
  • 2.6. Notes
    •

    CHAPTER 3. Countable MCs

  • 3.1. Introduction
  • 3.2. Classification of states and class properties
  • 3.3. Limit theorems
  • 3.4. Notes
    •

    CHAPTER 4. Harris MCs

  • 4.1. Introduction
  • 4.2. Basic notation and properties
  • 4.3. Characterization of Harris recurrence via occupation measures
  • 4.4  Sufficient conditions for P.H.R.
  • 4.5. Harrris and Doeblin decompositions
  • 4.6  Notes
    •

    CHAPTER 5. MCs in metric spaces

  • 5.1. Introduction
  • 5.2. The limit in ergodic theorems
  • 5.3. Yosida' ergodic decomposition
  • 5.4. Pathwise results
  • 5.5. Proofs
  • 5.6. Notes
    •

    CHAPTER 6. Classification of MCs via occupation measures

  • 6.1. Introduction
  • 6.2. A classification
  • 6.3. On the Birkhoff Individual Ergodic Theorem
  • 6.4. Notes
    •

    PART II. Further ergodicity properties.

    CHAPTER 7. Feller MCs

  • 7.1. Introduction
  • 7.2. Weak- and strong-Feller MCs
  • 7.3. Quasi Feller MCs
  • 7.4. Notes
    •

    CHAPTER 8. The Poisson equation

  • 8.1. Introduction
  • 8.2. The Poisson equation
  • 8.3. Canonical pairs
  • 8.4. The Cesaro-averages approach
  • 8.5. The Abelian approach
  • 8.6. Notes
    •

    CHAPTER 9. Strong and uniform ergodicity

  • 9.1. Introduction
  • 9.2. Strong and uniform ergodicity
  • 9.3. Weak and weak uniform ergodicity
  • 9.4. Notes

    • PART III. Existence and approximation of invariant p.m.'s

    CHAPTER 10. Existence and uniqueness of invariant p.m.'s

  • 10.1. Introduction
  • 10.2. Notation and definitions
  • 10.3. Existence results
  • 10.4. MCs in LCS metric spaces
  • 10.5. Other existence results in LCS metric spaces
  • 10.6 Technical preliminaries
  • 10.7. Proofs
  • 10.8. Notes
    •

    CHAPTER 11. Existence and uniqueness of fixed points for Markov operators

  • 11.1. Introduction
  • 11.2. Notation and definitions
  • 11.3. Existence results
  • 11.4. Proofs
  • 11.5. Notes
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    CHAPTER 12. Approximation proedures for invariant p.m.'s

  • 12.1. Introduction
  • 12.2. Statement of the problem and preliminaries
  • 12.3. An approximation scheme
  • 12.4. A moment approach for a special class of MCs
  • 12.5. Notes
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    BIBLIOGRAPHY

    INDEX