Markov Chains and Invariant Probabilities di Onésimo Hernández-Lerma, Jean B. Lasserre edito da Birkhäuser Basel
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Markov Chains and Invariant Probabilities

EAN:

9783764370008

ISBN:

3764370009

Pagine:
228
Formato:
Hardback
Lingua:
Tedesco
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Descrizione Markov Chains and Invariant Probabilities

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).

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