 On the ergodic decomposition for a class of Markov chainsO.L.V. Costa and F. Dufour Stochastic Processes and their Applications, 2005, vol. 115, issue 3, 401-415 Abstract: In this paper we present sufficient conditions for the Doeblin decomposition, and necessary and sufficient conditions for an ergodic decomposition for a Markov chain satisfying a T'-condition, which is a condition adapted from the paper (Statist. and Probab. Lett. 50 (2000) 13). Under no separability assumption on the [sigma]-field, it is shown that the T'-condition is sufficient for the condition that there are no uncountable disjoint absorbing sets and, under some hypothesis, it is also necessary. For the case in which the [sigma]-field is countable generated and separated, this condition is equivalent to the existence of a T continuous component for the Markov chain. Furthermore, under the assumption that the space is a compact separable metric space, it is shown that the Foster-Lyapunov criterion is necessary and sufficient for the existence of an invariant probability measure for the Markov chain, and that every probability measure for the Markov chain is, in this case, non-singular. Keywords: Markov; chain; Invariant; probability; measures; Countable; ergodic; decomposition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:115:y:2005:i:3:p:401-415 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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