Strong Stable Markov Chains

Looking at ergodicity and stability programs for homogeneous Markov chains with a discrete-time and with values in a measurable space, this book examines methods for the explicit evaluation of estimates for convergence rates in ergodic theorems and in stability theorems for wide classes of chains.

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01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.

This monograph presents a new approach to the investigation of ergodicity and stability problems for homogeneous Markov chains with a discrete-time and with values in a measurable space. The main purpose of this book is to highlight various methods for the explicit evaluation of estimates for convergence rates in ergodic theorems and in stability theorems for wide classes of chains. These methods are based on the classical perturbation theory of linear operators in Banach spaces and give new results even for finite chains.

In the first part of the book, the theory of uniform ergodic chains with respect to a given norm is developed. In the second part of the book the condition of the uniform ergodicity is removed.