Markov Chains - Rilegato

Douc, Randal; Moulines, Eric; Priouret, Pierre; Soulier, Philippe

Rilegato

ISBN 10: 3319977032 ISBN 13: 9783319977034

Casa editrice: Springer Nature, 2019

Riassunto

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 carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature.

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. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeperthan that needed to study countable state space (very little measure theory is required).

Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.

Su questo libro

Informazioni sull?autore

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 Curie

Philippe Soulier is a professor at Université de Paris-Nanterre

Dalla quarta di copertina

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 carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. 

Part I lays the foundations of the theory of Markov chain on general state-spaces. Part II covers the basic theory of irreducible Markov chains starting from the definition of small and petite sets, the characterization of recurrence and transience and culminating in the Harris theorem. Most of the results rely on the splitting technique which allows to reduce the theory of irreducible to a Markov chain with an atom. These two parts can serve as a text on Markov chain theory on general state-spaces. Although the choice of topics is quite different from what is usually covered in a classical Markov chain course, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all of these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). 

Part III deals with advanced topics on the theory of irreducible Markov chains, covering geometric and subgeometric convergence rates. Special attention is given to obtaining computable convergence bounds using Foster-Lyapunov drift conditions and minorization techniques. 

Part IV presents selected topics on Markov chains, covering mostly hot recent developments. It represents a biased selection of topics, reflecting the authors own research inclinations. This includes quantitative bounds of convergence in Wasserstein distances, spectral theory of Markov operators, central limit theorems for additive functionals and concentration inequalities.

Some of the results in Parts III and IV appear for the first time in book form and some are original.

Dettagli dell'edizione

• Editore: Springer Nature
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 3319977032
• ISBN 13: 9783319977034
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 757
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania