Markov Chains and Invariant Probabilities (Hardcover, 2003 ed.)

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).

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Mathematics, 211
Release date:	February 2003
First published:	2003
Authors:	Onesimo Hernandez-Lerma • Jean B. Lasserre
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Hardcover
Pages:	208
Edition:	2003 ed.
ISBN-13:	978-3-7643-7000-8
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
LSN:	3-7643-7000-9
Barcode:	9783764370008

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