Markov Chains and Invariant Probabilities

Hernandez-Lerma, Onesimo; Lasserre, Jean-Bernard

ISBN 10: 3764370009 / ISBN 13: 9783764370008

Published by Birkhauser Verlag AG, 2003

Concerning discrete-time homogeneous Markov chains that admit an invariant probability measure, this book aims to give a presentation on some key issues about the ergodic behavior of these chains. These issues include the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space. Series: Progress in Mathematics. Num Pages: 208 pages, biography. BIC Classification: PBWL. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 14. Weight in Grams: 486. . 2003. Hardback. . . . . Seller Inventory # V9783764370008

Synopsis:

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

From the Back Cover:

This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure. The main objective is to give a systematic, self-contained presentation on some key issues about the ergodic behavior of that class of Markov chains. These issues include, in particular, the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space. Some of the results presented appear for the first time in book form. A distinguishing feature of the book is the emphasis on the role of expected occupation measures to study the long-run behavior of Markov chains on uncountable spaces.

The intended audience are graduate students and researchers in theoretical and applied probability, operations research, engineering and economics.

Bibliographic Details

Title: Markov Chains and Invariant Probabilities
Publisher: Birkhauser Verlag AG
Publication Date: 2003
Binding: Hardcover
Condition: New