CONDITIONED, QUASI-STATIONARY, RESTRICTED MEASURES AND ESCAPE FROM METASTABLE STATES

• 成果类型: Article
• 署名作者: Fernandez, R.; Manzo, F.; Nardi, F. R.; Scoppola, E.; Sohier, J.
• 署名单位: Utrecht University; Roma Tre University; Eindhoven University of Technology; Eindhoven University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1102
• 发表日期: 2016
• 页码: 760-793
• 关键词: small transition-probabilities; reversible markov-chains; Stochastic dynamics; renormalization-group; kawasaki dynamics; general domain; random-walks; exit problem; Rare events; times

摘要

We study the asymptotic hitting time tau((n)) of a family of Markov processes X-(n) to a target set G((n)) when the process starts from a trap defined by very general properties. We give an explicit description of the law of X-(n) conditioned to stay within the trap, and from this we deduce the exponential distribution of tau((n).) Our approach is very broad-it does not require reversibility, the target G does not need to be a rare event and the traps and the limit on n can be of very general nature-and leads to explicit bounds on the deviations of tau((n)) from exponentially. We provide two nontrivial examples to which our techniques directly apply.