Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology

• 成果类型: Article
• 署名作者: Gosselin, F
• 署名单位: Universite PSL; Ecole Pratique des Hautes Etudes (EPHE); Institut Agro; Montpellier SupAgro; CIRAD; Centre National de la Recherche Scientifique (CNRS); Institut de Recherche pour le Developpement (IRD); Universite Paul-Valery; Universite de Montpellier
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/998926993
• 发表日期: 2001
• 页码: 261-284
• 关键词: quasi-stationary distributions; branching-processes; ergodic properties; limit-theorem

摘要

We find a Lyapunov-ty pe 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 Bienayme-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.