Iterated Brownian motion in bounded domains in R^n
| dc.creator | Nane, Erkan | |
| dc.date | 2005-05-02 | |
| dc.date | 2005-10-07 | |
| dc.date.accessioned | 2026-07-07T06:39:53Z | |
| dc.date.available | 2026-07-07T06:39:53Z | |
| dc.description | Let $τ_{D}(Z) $ is the first exit time of iterated Brownian motion from a domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[τ_{D}(Z) >t]$ be its distribution. In this paper we establish the exact asymptotics of $P_{z}[τ_{D}(Z) >t]$ over bounded domains as an extension of the result in DeBlassie \cite{deblassie}, for $z\in D$ $$ P_{z}[τ_{D}(Z)>t]\approx t^{1/2} \exp(-{3/2}π^{2/3}λ_{D}^{2/3}t^{1/3}), as t\to\infty . $$ We also study asymptotics of the life time of Brownian-time Brownian motion (BTBM), $Z^{1}_{t}=z+X(Y(t))$, where $X_{t}$ and $Y_{t}$ are independent one-dimensional Brownian motions. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505026 | |
| dc.identifier | http://arxiv.org/abs/math/0505026 | |
| dc.identifier | Stochastic Processes and Their Applications, 116 (2006), 905-916. | |
| dc.identifier | doi:10.1016/j.spa.2005.10.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101245 | |
| dc.subject | Probability | |
| dc.subject | 60J65, 60K99 | |
| dc.title | Iterated Brownian motion in bounded domains in R^n | |
| dc.type | text |