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