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Markov Chains [2018]
- 1
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Introduction
- 1
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Probability Background
- 3
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Markov Chains: Basic Definitions
- 11
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Preliminaries
- 27
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Examples of Markov Chains
- 39
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Gambling Problems
- 45
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Tools for Non-commuting Operators
- 53
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Stopping Times and the Strong Markov Property
- 61
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Multivariate Trace Inequalities
- 69
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Random Walks
- 75
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Approximate Quantum Markov Chains
- 75
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Martingales, Harmonic Functions and Poisson–Dirichlet Problems
- 89
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Discrete-Time Markov Chains
- 97
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Ergodic Theory for Markov Chains
- 115
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First Step Analysis
- 119
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Atomic Chains
- 145
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Markov Chains on a Discrete State Space
- 147
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Classification of States
- 163
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Long-Run Behavior of Markov Chains
- 165
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Convergence of Atomic Markov Chains
- 189
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Branching Processes
- 191
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Small Sets, Irreducibility, and Aperiodicity
- 211
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Continuous-Time Markov Chains
- 221
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Transience, Recurrence, and Harris Recurrence
- 241
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Splitting Construction and Invariant Measures
- 263
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Discrete-Time Martingales
- 265
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Feller and <Emphasis Type="BoldItalic">T</Emphasis>-Kernels
- 281
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Spatial Poisson Processes
- 289
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Rates of Convergence for Atomic Markov Chains
- 289
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Reliability Theory
- 313
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Geometric Recurrence and Regularity
- 339
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Geometric Rates of Convergence
- 361
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(<Emphasis Type="Italic">f</Emphasis>, <Emphasis Type="Italic">r</Emphasis>)-Recurrence and Regularity
- 385
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Subgeometric Rates of Convergence
- 401
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Uniform and <Emphasis Type="Italic">V</Emphasis>-Geometric Ergodicity by Operator Methods
- 421
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Coupling for Irreducible Kernels
- 455
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Convergence in the Wasserstein Distance
- 489
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Central Limit Theorems
- 523
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Spectral Theory
- 575
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Concentration Inequalities