Sanz-Solé, MartaViles, Noèlia2019-10-242019-10-242017-060304-4149https://hdl.handle.net/2445/142997We 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.32 p.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esAplicacions de GaussEquacions diferencials parcials estocàstiquesGauss mapsStochastic partial differential equationsinfo:eu-repo/semantics/article6768882019-10-24info:eu-repo/semantics/openAccess