Ergodic Behavior of Markov Processes: With Applications to Limit Theorems

ISBN-13: 9783110458701 / Angielski / Twarda / 2017 / 267 str.

Alexei Kulik

Opis

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 Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems

Recenzje

"This book is clearly written, with many examples, and will be of interest to advanced students and researchers who wish to learn more about quantitative ergodic theory for Markov processes."
Max Fathi in: Mathematical Reviews Clippings (2019) MR3791835

O autorze

Alexei Kulik, National Academy of Sciences, Ukraine.