Thick points for the Cauchy process
| dc.creator | Daviaud, Olivier | |
| dc.date | 2003-10-18 | |
| dc.date.accessioned | 2026-07-07T05:02:05Z | |
| dc.date.available | 2026-07-07T05:02:05Z | |
| dc.description | Let $\mathcal{T}(x,\eps)$ denote the occupation measure of an interval of length $2\eps$ centered at $x$ by the Cauchy process run until it hits $(-\infty,-1]\cup [1,\infty)$. We prove that $\sup_{|x|\leq 1}\mathcal{T}(x,\eps)/(\eps(\ln\eps)^2)\to 2/π$ a.s. as $\eps\to 0$. We also obtain the multifractal spectrum for thick points, i.e. the Hausdorff dimension of the set of $α$-thick points $x$ for which $\lim_{\eps \to 0} \mathcal{T}(x,\eps)/(\eps(\ln\eps)^2) = α> 0$. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310298 | |
| dc.identifier | http://arxiv.org/abs/math/0310298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68914 | |
| dc.subject | Probability | |
| dc.subject | 60J55 | |
| dc.title | Thick points for the Cauchy process | |
| dc.type | text |