On weak lumpability of denumerable Markov chains
type: Item
instance of: scholarly article
title: On weak lumpability of denumerable Markov chains
zbMATH Open document ID: 0843.60060
DOI: 10.1016/0167-7152(94)00238-5
author: James Ledoux
published in: Statistics \& Probability Letters
publication date: 1996-08-13T00:00:00Z
review text: The paper extends the results of \textit{G. Rubino} and \textit{B. Sericola} [J. Appl. Probab. 26, No. 3, 446-457 (1989; Zbl 0689.60065), Stochastic Processes Appl. 38, No. 2, 195-204 (1991; Zbl 0741.60065) and ibid. 45, No. 1, 115-125 (1993; Zbl 0764.60076)] and the author, \textit{G. Rubino} and \textit{B. Sericola} [J. Appl. Probab. 31, No. 3, 626-634 (1994; Zbl 0812.60055)] on weak lumpability of Markov chains with finite state space to denumerable Markov chains (with discrete or continuous time parameter). The problem: For a given homogeneous Markov chain the set of all initial distributions, which lead to an aggregated Markov chain with respect to a partition of the state space, is to find. In case that this set is not empty and an invariant or a quasistationary distribution exists, explicit descriptions of the aggregated Markov chain are derived.
reviewed by: Wilfried Schenk
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 844752
zbMATH Keywords: weak lumpability
zbMATH Keywords: positive recurrence
zbMATH Keywords: \(R\)-positivity
zbMATH Keywords: quasi-stationary distribution
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)00238-5
OpenAlex ID: W4299797081
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Wikidata QID: Q127174021
description: scientific article; zbMATH DE number 844752