Ergodic behavior of Markov processes : with applications to limit theorems / Alexei Kulik.

Format:

Book

Author/Creator:

Kulik, Alexei, author.

Series:

De Gruyter studies in mathematics ; Volume 67.

De Gruyter Studies in Mathematics, 01790986 ; Volume 67

Language:

English

Subjects (All):

Markov processes--Textbooks.

Markov processes.

Physical Description:

1 online resource (268 pages).

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2018.

Language Note:

In English.

Summary:

The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and ProcessesMarkov Chains with Discrete State SpacesGeneral Markov Chains: Ergodicity in Total VariationMarkovProcesseswithContinuousTimeWeak Ergodic Rates Part II: Limit TheoremsThe Law of Large Numbers and the Central Limit TheoremFunctional Limit Theorems

Contents:

Frontmatter

Preface

Contents

Introduction

Part I: Ergodic Rates for Markov Chains and Processes

1. Markov Chains with Discrete State Spaces

2. General Markov Chains: Ergodicity in Total Variation

3. Markov Processes with Continuous Time

4. WeakErgodicRates

Part II: Limit Theorems

5. The Law of Large Numbers and the Central Limit Theorem

6. Functional Limit Theorems

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (EBC, viewed December 22, 2017).

ISBN:

9783110458718

3110458713

OCLC:

1024011121