Occupation densities for SPDE's with reflection
| dc.creator | Zambotti, Lorenzo | |
| dc.date | 2002-04-25 | |
| dc.date.accessioned | 2026-07-07T04:48:05Z | |
| dc.date.available | 2026-07-07T04:48:05Z | |
| dc.description | We consider the solution (u,η) of the white-noise driven stochastic partial differential equation with reflection on the space interval [0,1] introduced by Nualart and Pardoux. First, we prove that at any fixed time t>0, the measure η([0,t]\times dθ) is absolutely continuous w.r.t. the Lebesgue measure dθon (0,1). We characterize the density as a family of additive functionals of u, and we interpret it as a renormalized local time at 0 of (u(t,θ))_{t\geq 0}. Finally we study the behaviour of ηat the boundary of [0,1]. The main technical novelty is a projection principle from the Dirichlet space of a Gaussian process, vector-valued solution of a linear SPDE, to the Dirichlet space of the process u. | |
| dc.identifier | https://arxiv.org/abs/math/0204313 | |
| dc.identifier | http://arxiv.org/abs/math/0204313 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63914 | |
| dc.subject | Probability | |
| dc.subject | 60H15; 60J55 | |
| dc.title | Occupation densities for SPDE's with reflection | |
| dc.type | text |