Markov Chains
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- Artikel-Nr.: 10475709
Beschreibung
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.
Eigenschaften
Breite: | 164 |
Gewicht: | 1413 g |
Höhe: | 244 |
Länge: | 43 |
Seiten: | 757 |
Sprachen: | Englisch |
Autor: | Eric Moulines, Philippe Soulier, Pierre Priouret, Randal Douc |
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