Iterated Brownian Motion in Parabola-Shaped Domains
| dc.creator | Nane, Erkan | |
| dc.date | 2004-04-27 | |
| dc.date | 2005-08-29 | |
| dc.date.accessioned | 2026-07-07T06:30:09Z | |
| dc.date.available | 2026-07-07T06:30:09Z | |
| dc.description | Iterated Brownian motion $Z_{t}$ serves as a physical model for diffusions in a crack. If $τ_{D}(Z) $ is the first exit time of this processes from a domain $D \subset \RR{R}^{n}$, started at $z\in D$, then $P_{z}[τ_{D}(Z)>t]$ is the distribution of the lifetime of the process in $D$. In this paper we determine the large time asymptotics of $P_{z}[τ_{P_α}(Z) > t]$ which gives exponential integrability of $τ_{P_α}(Z) $ for parabola-shaped domains of the form $ P_α=\{(x,Y)\in \RR{R} \times \RR{R}^{n-1}: x>0, |Y|<Ax^α \}$, for $ 0<α<1$, $A>0.$ We also obtain similar results for twisted domains in $\RR{R}^{2}$ as defined in \cite{DSmits}. In particular, for a planar iterated Brownian motion in a parabola $\mathcal{P}=\{(x,y): x>0, |y|< \sqrt{x} \}$ we find that for $z\in \mathcal{P}$ $$\lim_{t\to\infty} t^{-{1/7}} \log P_{z}[τ_{\mathcal{P}}(Z) >t]= - \frac{7 π^{2}}{2^{25/ 7}}. $$ | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404495 | |
| dc.identifier | http://arxiv.org/abs/math/0404495 | |
| dc.identifier | Potential Analysis, 24 (2006) , 105-123. | |
| dc.identifier | doi:10.1007/s11118-005-2611-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98271 | |
| dc.subject | Probability | |
| dc.subject | 60E99; 62E20 | |
| dc.title | Iterated Brownian Motion in Parabola-Shaped Domains | |
| dc.type | text |