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February 2001 Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology
Frèdèric Gosselin
Ann. Appl. Probab. 11(1): 261-284 (February 2001). DOI: 10.1214/aoap/998926993

Abstract

We find a Lyapunov-type sufficient condition for discrete-time Markov chains on a countable state space including an absorbing set to almost surely reach this absorbing set and to asymptotically stabilize conditional on nonabsorption. This result is applied to Bienaymè-Galton-Watson-like branching processes in which the offspring distribution depends on the current population size. This yields a generalization of the Yaglom limit. The techniques used mainly rely on the spectral theory of linear operators on Banach spaces and especially on the notion of quasi-compact linear operator.

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Frèdèric Gosselin. "Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology." Ann. Appl. Probab. 11 (1) 261 - 284, February 2001. https://doi.org/10.1214/aoap/998926993

Information

Published: February 2001
First available in Project Euclid: 27 August 2001

zbMATH: 1019.60082
MathSciNet: MR1825466
Digital Object Identifier: 10.1214/aoap/998926993

Subjects:
Primary: 60J10
Secondary: 47B37 , 47B65 , 60J20 , 60J85 , 92D25

Keywords: absorbing set , Bienaymè-Galton-Watson branching processes , conservation biology , demography , density-dependence , extinction , homogeneous Markov chain , infinite dimensional matrix , irreducible matrix , Lyapunov-type condition , nonnegative operator , Population dynamics , population viability analysis , population-size-dependent , quasi-compact linear operator , quasi-stationary distribution , Spectral theory , Yaglom limit

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 1 • February 2001
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