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Systems of stochastic Poisson equations: Hitting probabilities

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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.

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Stochastic Processes and their Applications, 2017, vol. 128, num. 6, p. 1857-1888

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Systems of stochastic Poisson equations: Hitting probabilities