We study the asymptotic hitting time τ (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 τ (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 τ (n) from exponentially.We provide two nontrivial examples to which our techniques directly apply.

Conditioned, quasi-stationary, restricted measures and escape from metastable states / Fernandez, R.; Manzo, F.; Nardi, F.R.; Scoppola, E.; Sohier, J.. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 26:(2016), pp. 760-793. [10.1214/15-AAP1102]

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

NARDI, FRANCESCA ROMANA;
2016

Abstract

We study the asymptotic hitting time τ (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 τ (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 τ (n) from exponentially.We provide two nontrivial examples to which our techniques directly apply.
2016
26
760
793
Fernandez, R.; Manzo, F.; Nardi, F.R.; Scoppola, E.; Sohier, J.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1078679
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