Conditioned, quasi-stationary, restricted measures and escape from metastable states

R. Fernández, F. Manzo, F.R. Nardi, E. Scoppola, J. Sohier

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

We study the asymptotic hitting time τ (n) τ(n) of a family of Markov processes X (n) X(n) to a target set G (n) 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) X(n) conditioned to stay within the trap, and from this we deduce the exponential distribution of τ (n) τ(n). Our approach is very broad—it does not require reversibility, the target G G does not need to be a rare event and the traps and the limit on n n can be of very general nature—and leads to explicit bounds on the deviations of τ (n) τ(n) from exponentially. We provide two nontrivial examples to which our techniques directly apply.
Original languageEnglish
Pages (from-to)760-793
JournalThe Annals of Applied Probability
Volume26
Issue number2
DOIs
Publication statusPublished - 2016

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