STOCHASTIC APPROXIMATION OF QUASI-STATIONARY DISTRIBUTIONS ON COMPACT SPACES AND APPLICATIONS

• 成果类型: Article
• 署名作者: Benaim, Michel; Cloez, Bertrand; Panloup, Fabien
• 署名单位: Institut Agro; Montpellier SupAgro; Universite de Montpellier; INRAE; Universite d'Angers
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1360
• 发表日期: 2018
• 页码: 2370-2416
• 关键词: fleming-viot processes; particle system; DIFFUSIONS; STABILITY; algorithm

摘要

As a continuation of a recent paper, dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact metric space killed in finite time. The idea is to run the process until extinction and then to bring it back to life at a position randomly chosen according to the (possibly weighted) empirical occupation measure of its past positions. General conditions are given ensuring the convergence of this measure to the quasi-stationary distribution of the chain. We then apply this method to the numerical approximation of the quasi-stationary distribution of a diffusion process killed on the boundary of a compact set. Finally, the sharpness of the assumptions is illustrated through the study of the algorithm in a nonirreducible setting.