Aysmptotic Behavior of Absorbing Markov Chains Conditional on Nonabsorption for Applications in Conservation Biology
Open Access
- 1 February 2001
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 11 (1) , 261-284
- https://doi.org/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.Keywords
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