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Title: | Systems of stochastic Poisson equations: Hitting probabilities |
Author: | Sanz-Solé, Marta Viles, Noèlia |
Keywords: | Aplicacions de Gauss Equacions diferencials parcials estocàstiques Gauss maps Stochastic partial differential equations |
Issue Date: | Jun-2017 |
Publisher: | Elsevier B.V. |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.spa.2017.08.014 |
It is part of: | Stochastic Processes and their Applications, 2017, vol. 128, num. 6, p. 1857-1888 |
URI: | http://hdl.handle.net/2445/142997 |
Related resource: | https://doi.org/10.1016/j.spa.2017.08.014 |
ISSN: | 0304-4149 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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