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Markov Chains: Analytic and Monte Carlo Computations

Author Carl Graham
Release Date: 2014/05/01
ISBN: 9781118882696
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Book Description

Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features:

  • Numerous exercises with solutions as well as extended case studies.

  • A detailed and rigorous presentation of Markov chains with discrete time and state space.

  • An appendix presenting probabilistic notions that are necessary to the reader, as well as giving more advanced measure-theoretic notions.

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    Table of Contents

    1. Cover
    2. Wiley Series in Probability and Statistics
    3. Title Page
    4. Copyright
    5. Preface
    6. List of Figures
    7. Nomenclature
      1. Acronyms
      2. Symbols
    8. Introduction
    9. Chapter 1: First steps
      1. 1.1 Preliminaries
      2. 1.2 First properties of Markov chains
      3. 1.3 Natural duality: algebraic approach
      4. 1.4 Detailed examples
      5. Exercises
    10. Chapter 2: Past, present, and future
      1. 2.1 Markov property and its extensions
      2. 2.2 Hitting times and distribution
      3. 2.3 Detailed examples
      4. Exercises
    11. Chapter 3: Transience and recurrence
      1. 3.1 Sample paths and state space
      2. 3.2 Invariant measures and recurrence
      3. 3.3 Complements
      4. Exercises
    12. Chapter 4: Long-time behavior
      1. 4.1 Path regeneration and convergence
      2. 4.2 Long-time behavior of the instantaneous laws
      3. 4.3 Elements on the rate of convergence for laws
      4. Exercises
    13. Chapter 5: Monte Carlo methods
      1. 5.1 Approximate solution of the Dirichlet problem
      2. 5.2 Invariant law simulation
    14. Appendix A: Complements
      1. A.1 Basic probabilistic notions
      2. A.2 Discrete measure convergence
      3. A.3 Measure-theoretic framework
    15. References
    16. Solutions for the exercises
      1. Solutions for Chapter 1
      2. Solutions for Chapter 2
    17. Solutions for the exercises
      1. Solutions for Chapter 3
      2. Solutions for Chapter 4
    18. Index
    19. Wiley Series in Probability and Statistics
    20. End User License Agreement
    18.191.162.51