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 nontrivial examples to which our techniques directly apply.
Citation
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. https://doi.org/10.1214/15-AAP1102
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