Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology
type: Item
instance of: scholarly article
title: Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology
zbMATH Open document ID: 1019.60082
author: Frédéric Gosselin
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: Discrete-time Markov chains on a countable state space are considered which include an absorbing set. A Lyapunov-type sufficient condition is given for the Markov chain to almost surely reach the absorbing set and to asymptotically stabilize conditional on nonabsorption, hence generalizing results about the existence of a Yaglom limit. The results are applied to population-size-dependent Bienaymé-Galton-Watson branching processes in which the offspring distribution depends on the current population size. The results are based on linear operator theory, and especially on the notion of quasi-compact operator. This imposes a rather stringent assumption on the Markov chain but leads to the formulation of sufficient conditions that appear to be biologically realistic and verifiable.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 47N30
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1906262
zbMATH Keywords: Bienaymé-Galton-Watson process
zbMATH Keywords: Yaglom limit
zbMATH Keywords: absorbing set
zbMATH Keywords: quasi-compact linear operator
reviewed by: Annette Kopp-Schneider
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/998926993
OpenAlex ID: W2011490656
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DOI: 10.1214/AOAP/998926993
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description: scientific article; zbMATH DE number 1906262