Markov Chains and Invariant Probabilities (Progress in Mathematics, 211, Band 211)

Hernández-Lerma, Onésimo and Jean B. Lasserre:

ISBN 10: 3764370009 / ISBN 13: 9783764370008

Published by Birkhäuser 24.02.2003., 2003

About this Item

224 Seiten Mit leichten altersbedingten Lager- und Gebrauchsspuren. Biblitoheksex. U-25 Sprache: Englisch Gewicht in Gramm: 495 15,6 x 1,4 x 23,4 cm, Gebundene Ausgabe.

Seller Inventory # 120649

Bibliographic Details

• Title: Markov Chains and Invariant Probabilities (Progress in Mathematics, 211, Band 211)
• Publisher: Birkhäuser 24.02.2003.
• Publication Date: 2003
• Language: English
• ISBN 10: 3764370009
• ISBN 13: 9783764370008
• Binding: Hardcover
• Edition: Auflage: 2003.
• Condition: Gut
• Seller catalogs:
  • Wissenschaft

About this title

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.