On the existence of a quasistationary measure for a Markov chain
type: Item
instance of: scholarly article
title: On the existence of a quasistationary measure for a Markov chain
zbMATH Open document ID: 1018.60071
author: Charles E. M. Pearce
author: Jean B. Lasserre
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: The paper continues earlier investigations done by the authors and others. The topic relates to Markov chains on a locally compact separable metric space \(X\) each of them having a weak Fellerian transition kernel \(P\) and an absorbing set of states \(S\). The main result concerns necessary and sufficient conditions under which for such a chain a quasistationary probability distribution \(\nu\) exists (that is, \(\nu\) satisfies \(\nu(B) = \frac{\int P(x;B)\nu(dx)}{\int P(x;X\setminus S)\nu(dx)}\), \(B\) a Borel set, \(B\cap S =\emptyset\)). Further it is discussed how two different cases, the one considered by G. Høgnas (1997), the other by \textit{P. A. Ferrari, H. Kesten, S. Martinez} and \textit{D. Picco} [Ann. Probab. 23, No.~2, 501-521 (1995; Zbl 0827.60061)] are included.
reviewed by: Wilfried Schenk
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 1905987
zbMATH Keywords: Markov chain
zbMATH Keywords: absorption set
zbMATH Keywords: quasistationary distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1008956338
OpenAlex ID: W1863632028
cites work: Generalizations of Farkas’ Theorem
cites work: Q4283467
cites work: Q5336643
cites work: Existence of quasi-stationary distributions: A renewal dynamical approach
cites work: Mathematical Methods of Economics
cites work: Ergodic theorems and ergodic decomposition for Markov chains
cites work: On the quasi-stationary distribution of a stochastic Ricker model
cites work: A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps
cites work: Existence and uniqueness of an invariant probability for a class of Feller Markov chains
cites work: Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state
cites work: Q5593890
cites work: On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
cites work: Exponential decay and ergodicity of general Markov processes and their discrete skeletons
cites work: R-theory for Markov chains on a general state space. I: Solidarity properties and R-recurrent chains
DOI: 10.1214/AOP/1008956338
description: scientific article; zbMATH DE number 1905987