Systems of stochastic Poisson equations: Hitting probabilities |
| |
Authors: | Marta Sanz-Solé Noèlia Viles |
| |
Institution: | 1. Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain;2. @DiMedia, Actividades Digital Media, Avinguda Diagonal, 477, 08036 Barcelona, Spain |
| |
Abstract: | We consider a -dimensional random field that solves a system of elliptic stochastic equations on a bounded domain , with additive white noise and spatial dimension . Properties of and its probability law are proved. For Gaussian solutions, using results from Dalang and Sanz-Solé (2009), we establish upper and lower bounds on hitting probabilities in terms of the Hausdorff measure and Bessel–Riesz capacity, respectively. This relies on precise estimates of the canonical distance of the process or, equivalently, on estimates of increments of the Green function of the Laplace equation. |
| |
Keywords: | primary 60H15 60G15 60J45 secondary 60G60 60H07 Systems of stochastic Poisson equations Hitting probabilities Capacity Hausdorff measure |
本文献已被 ScienceDirect 等数据库收录! |
|