Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/142997
Systems of stochastic Poisson equations: Hitting probabilities
Journal Title
Authors
Director/Tutor
Additional contribution
Journal ISSN
Volume Title
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.
Related resource
Subject (English)
Citation
Citation
SANZ-SOLÉ, Marta and VILES, Noèlia. Systems of stochastic Poisson equations: Hitting probabilities. Stochastic Processes and their Applications. 2017. Vol. 128, num. 6, pags. 1857-1888. ISSN 0304-4149. [consulted: 13 of October of 2026]. Available at: https://hdl.handle.net/2445/142997