Markov Chains
This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained while all the results are carefull...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing,
2018.
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| Edition: | 1st ed. 2018. |
| Series: | Springer Series in Operations Research and Financial Engineering,
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| Subjects: | |
| ISBN: | 9783319977041 |
| ISSN: | 1431-8598 |
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Table of Contents:
- Part I Foundations
- Markov Chains: Basic Definitions
- Examples of Markov Chains
- Stopping Times and the Strong Markov Property
- Martingales, Harmonic Functions and Polsson-Dirichlet Problems
- Ergodic Theory for Markov Chains
- Part II Irreducible Chains: Basics
- Atomic Chains
- Markov Chains on a Discrete State Space
- Convergence of Atomic Markov Chains
- Small Sets, Irreducibility and Aperiodicity
- Transience, Recurrence and Harris Recurrence
- Splitting Construction and Invariant Measures
- Feller and T-kernels
- Part III Irreducible Chains: Advanced Topics
- Rates of Convergence for Atomic Markov Chains
- Geometric Recurrence and Regularity
- Geometric Rates of Convergence
- (f, r)-recurrence and Regularity
- Subgeometric Rates of Convergence
- Uniform and V-geometric Ergodicity by Operator Methods
- Coupling for Irreducible Kernels
- Part IV Selected Topics
- Convergence in the Wasserstein Distance
- Central Limit Theorems
- Spectral Theory
- Concentration Inequalities
- Appendices
- A Notations
- B Topology, Measure, and Probability
- C Weak Convergence
- D Total and V-total Variation Distances
- E Martingales
- F Mixing Coefficients
- G Solutions to Selected Exercises.