DEGENERATE PROCESSES KILLED AT THE BOUNDARY OF A DOMAIN

• 成果类型: Article
• 署名作者: Benaim, Michel; Champagnat, Nicolas; Ocafrain, William; Villemonais, Denis
• 署名单位: University of Neuchatel; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Inria; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1720
• 发表日期: 2025
• 页码: 720-752
• 关键词: quasi-stationary distributions; one-dimensional diffusions; Exponential convergence; harnack inequality; Operators; uniqueness; BEHAVIOR; time

摘要

We investigate quasi-stationarity properties of Feller processes that are killed when exiting a relatively compact set. Our main result provides general conditions ensuring that such a process possesses a (possibly nonunique) quasi-stationary distribution. Conditions ensuring uniqueness and exponential convergence are discussed. Our conditions are well suited to the study of degenerate processes, such as nonelliptic diffusions or piecewise deterministic Markov processes (PDMP). The results are applied to stochastic differential equations, and we illustrate the application to PDMPs with an example.