Exponential convergence to quasi-stationary distribution and Q-process

• 成果类型: Article
• 署名作者: Champagnat, Nicolas; Villemonais, Denis
• 署名单位: Universite de Lorraine; Inria
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0611-7
• 发表日期: 2016
• 页码: 243-283
• 关键词: time; EXISTENCE; INFINITY

摘要

For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death processeswith catastrophes, multi-dimensional birth and death processes, infinite-dimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain.