Let $D$ be the interior of a parabola in $\mathbb{R}^2$ and $\tau_D$
the first exit time of Brownian motion from $D$ .We show $.-log P(\tau_D)
>t)$ behaves like $t^{1 /3}$ as $t \to \infty$.
Publié le : 2001-04-14
Classification:
Exit times,
eigenfunction expansions,
Feynman-Kac functionals,
Bessel processes,
large deviation,
60J65,
60J50,
60F10.
@article{1008956696,
author = {Ba\~nuelos, Rodrigo and DeBlassie, R.Dante and Smits, Robert},
title = {The First Exit Time of Planar Brownian Motion from The Interior Of
a Parabola},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 882-901},
language = {en},
url = {http://dml.mathdoc.fr/item/1008956696}
}
Bañuelos, Rodrigo; DeBlassie, R.Dante; Smits, Robert. The First Exit Time of Planar Brownian Motion from The Interior Of
a Parabola. Ann. Probab., Tome 29 (2001) no. 1, pp. 882-901. http://gdmltest.u-ga.fr/item/1008956696/