SPD

Abstract

We will give some criteria which yield upper and lower bounds for the hitting probabilities of random fields in terms of Hausdorff measure an Bessel-Riesz capacity, respectively. Firstly, the results will be applied to systems of stochastic wave equations in arbitrary spatial dimension, driven by a multidimensional additive Gaussian noise, white in time and colored in space. In a second part, we shall consider spatial dimensions $k\le 3$. We will report on work in progress concerning some extensions to systems driven by multiplicative noise. This is joint work with R. Dalang (EPFL, Switzerland).