2009 Probability Seminar - 13

A basic question in probabilistic potential theory is the following: Consider a random proper subset K of R^d, for what nonrandom sets A is P{K intersect A not equal 0}? In this lecture we will give some abstract results when K is the range of a random field {v(x), x in I}, I is proper subset of R^k. More specically, we will establish upper and lower bounds of the hitting probabilities in terms of the Hausdor measure and the Bessel-Riesz capacity of A, respectively, and highlight the role of the dimensions d and k. Application to systems of stochastic wave equations will be discussed.