UNIFORM CONVERGENCE OF THE FLEMING-VIOT PROCESS IN A HARD KILLING METASTABLE CASE

• 成果类型: Article
• 署名作者: Journel, Lucas; Monmarche, Pierre
• 署名单位: University of Neuchatel; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2134
• 发表日期: 2025
• 页码: 1019-1048
• 关键词: quasi-stationary distributions; stochastic-approximation; diffusion-processes; MARKOV-PROCESSES; particle system; limit

摘要

We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a coupling argument, we establish the longtime convergence of the Fleming-Viot process toward some stationary measure at an exponential rate independent of N, the size of the system, as well as uniform in time propagation of chaos estimates.