Lifetime asymptotics of iterated Brownian motion in R^{n}
| dc.creator | Nane, Erkan | |
| dc.date | 2006-03-28 | |
| dc.date.accessioned | 2026-07-07T08:07:41Z | |
| dc.date.available | 2026-07-07T08:07:41Z | |
| dc.description | Let $τ_{D}(Z) $ be 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 improvement of the results in \cite{deblassie, nane2}, for $z\in D$ \begin{eqnarray} \lim_{t\to\infty} t^{-1/2}\exp({3/2}π^{2/3}λ_{D}^{2/3}t^{1/3}) P_{z}[τ_{D}(Z)>t]= C(z),\nonumber \end{eqnarray} where $C(z)=(λ_{D}2^{7/2})/\sqrt{3 π}(ψ(z)\int_{D}ψ(y)dy) ^{2}$. Here $λ_{D}$ is the first eigenvalue of the Dirichlet Laplacian ${1/2}Δ$ in $D$, and $ψ$ is the eigenfunction corresponding to $λ_{D}$ . We also study lifetime asymptotics 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.identifier | https://arxiv.org/abs/math/0603637 | |
| dc.identifier | http://arxiv.org/abs/math/0603637 | |
| dc.identifier | ESAIM: P&S, March 2007, Vol. 11, pp. 147-160 | |
| dc.identifier | doi:10.1051/ps:2007012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131014 | |
| dc.subject | Probability | |
| dc.subject | 60J65; 60K99 | |
| dc.title | Lifetime asymptotics of iterated Brownian motion in R^{n} | |
| dc.type | text |