Let $X_t$ be Brownian motion on a Riemannian manifold $M$ started at $m$ and let $T$ be the first time $X_t$ exits a normal ball about $m$. The first exit time $T$ for $M = S^3 \times H^3$ has the same distribution as the first exit time for $M = \mathbf{R}^6$. For $M = S^3 \times H^3, T$ and $X_T$ are independent random variables.
Publié le : 1992-04-14
Classification:
Brownian motion,
diffusions on manifolds,
exit time and place,
transformation of drift,
58G32,
60J65,
53B20
@article{1176989797,
author = {Hughes, H. R.},
title = {Brownian Exit Distributions from Normal Balls in $S^3 \times H^3$},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 655-659},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989797}
}
Hughes, H. R. Brownian Exit Distributions from Normal Balls in $S^3 \times H^3$. Ann. Probab., Tome 20 (1992) no. 4, pp. 655-659. http://gdmltest.u-ga.fr/item/1176989797/