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

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

Research output: Book/ReportReportAcademic

79 Downloads (Pure)

Abstract

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 non trivial examples to which our techniques directly apply.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages39
Publication statusPublished - 2014

Publication series

NameReport Eurandom
Volume2014019
ISSN (Print)1389-2355

Fingerprint Dive into the research topics of 'Conditioned, quasi-stationary, restricted measures and escape from metastable states'. Together they form a unique fingerprint.

Cite this