Markov Chains and Invariant Probabilities |
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| Author:
| Hernández-Lerma, Onésimo
Lasserre, Jean B. |
| Series title: | Progress in Mathematics Ser. |
| ISBN: | 978-3-0348-9408-1 |
| Publication Date: | Oct 2012 |
| Publisher: | Springer Basel AG
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| Book Format: | Paperback |
| List Price: | USD $54.99 |
Book Description:
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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...
More DescriptionThis 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).