Properties of the density for a three dimensional stochastic wave equation
| dc.creator | Sanz-Solé, Marta | |
| dc.date | 2008-02-12 | |
| dc.date.accessioned | 2026-07-07T09:20:13Z | |
| dc.date.available | 2026-07-07T09:20:13Z | |
| dc.description | We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let $p_{t,x}(y)$ be the density of the law of the solution $u(t,x)$ of such an equation at points $(t,x)\in]0,T]\times \IR^3$. We prove that the mapping $(t,x)\mapsto p_{t,x}(y)$ owns the same regularity as the sample paths of the process $\{u(t,x), (t,x)\in]0,T]\times \mathbbR^3\}$ established Dalang and Sanz-Solé [Memoirs of the AMS, to appear]. The proof relies on Malliavin calculus and more explicitely, Watanabe's integration by parts formula and estimates derived form it. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/0802.1607 | |
| dc.identifier | http://arxiv.org/abs/0802.1607 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154653 | |
| dc.subject | Probability | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 60H15, 60H07, 60G60, 60G17, 35L05 | |
| dc.title | Properties of the density for a three dimensional stochastic wave equation | |
| dc.type | text |