Markov Chains

Inbunden, Engelska, 2019

AvRandal Douc,Eric Moulines,Pierre Priouret,Philippe Soulier

1 179 kr

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This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques.

Produktinformation

Utgivningsdatum2019-01-03
Mått155 x 235 x 37 mm
Vikt1 388 g
FormatInbunden
SpråkEngelska
SerieSpringer Series in Operations Research and Financial Engineering
Antal sidor757
FörlagSpringer International Publishing AG
ISBN9783319977034

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Randal Douc is a Professor in the CITI Department at Telecom SudParis. His research interests include parameter estimation in general Hidden Markov models and Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo methods.Eric Moulines is a Professor at Ecole Polytechnique's Applied Mathematics Center (CMAP, UMR Ecole Polytechnique/CNRS). Pierre Priouret is a Professor at Université Pierre et Marie CuriePhilippe Soulier is a professor at Université de Paris-Nanterre

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.