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April 2016 Conditioned, quasi-stationary, restricted measures and escape from metastable states
R. Fernandez, F. Manzo, F. R. Nardi, E. Scoppola, J. Sohier
Ann. Appl. Probab. 26(2): 760-793 (April 2016). DOI: 10.1214/15-AAP1102


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.


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R. Fernandez. F. Manzo. F. R. Nardi. E. Scoppola. J. Sohier. "Conditioned, quasi-stationary, restricted measures and escape from metastable states." Ann. Appl. Probab. 26 (2) 760 - 793, April 2016.


Received: 1 October 2014; Revised: 1 February 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1339.60110
MathSciNet: MR3476624
Digital Object Identifier: 10.1214/15-AAP1102

Primary: 60J27, 60J28, 82C05

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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