We study the lifetime of a conditioned diffusion (or $h$-path) on a bounded $C^\infty$ domain $G$ in $\mathbb{R}^d$. Making use of results of Donsker and Varadhan, we show that the tail of the distribution of the lifetime decays exponentially; in fact, the decay constant is the same as that for the exponential decay of the tail of the distribution of the first time the unconditioned diffusion exits $G$. In the case of Brownian motion and bounded domains (not necessarily $C^\infty$) we describe some sufficient conditions to ensure the previously described asymptotic results hold here too.
Publié le : 1988-07-14
Classification:
Conditioned diffusions,
$h$-paths,
lifetime,
large deviations,
Donsker-Varadhan $I$-function,
60J60,
60J65
@article{1176991678,
author = {DeBlassie, R. Dante},
title = {Doob's Conditioned Diffusions and their Lifetimes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1063-1083},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991678}
}
DeBlassie, R. Dante. Doob's Conditioned Diffusions and their Lifetimes. Ann. Probab., Tome 16 (1988) no. 4, pp. 1063-1083. http://gdmltest.u-ga.fr/item/1176991678/