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Anisotropic Gaussian random fields: criteria for hitting probabilities and applications

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We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and Hausdorff measure, respectively, therefore extending the classical estimates with the Bessel-Riesz capacity and the $\gamma$ -dimensional Hausdorff measure. We apply the criteria to a system of linear stochastic partial differential equations driven by space-time noises that are fractional in time and either white or colored in space.

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Stochastics And Partial Differential Equations-Analysis And Computations, 2021

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Anisotropic Gaussian random fields: criteria for hitting probabilities and applications