Markov Chains and Invariant Probabilities (Progress in Mathematics)

Hernández-Lerma, Onésimo; Lasserre, Jean B.

ISBN 10: 3034894082 / ISBN 13: 9783034894081

Editore: Birkhäuser, 2012

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Codice articolo ABLIING23Mar3113020038687

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Titolo: Markov Chains and Invariant Probabilities (...

Casa editrice: Birkhäuser

Data di pubblicazione: 2012

Legatura: Brossura

Condizione: New

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Riassunto:

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).

Recensione:

"It should be stressed that an important part of the results presented is due to the authors. . . . In the reviewer's opinion, this is an elegant and most welcome addition to the rich literature of Markov processes."

--MathSciNet