Prof. dr. Marta Sanz-Solé: Deterministic sets visited by random trajectories
Source: Mathematics colloquium
Univerza v Barceloni
Predsednica evropskega matematičnega društva
We are interested in geometric measure properties of deterministic sets hit by random fields. More specifically, we will analyze conditions which provide upper and lower bounds for hitting probabilities of random fields in terms of the Hausdorff measure and the Bessel-Riesz capacity of the deterministic sets, respectively. The role of the regularity of the random fields, and the properties of probability densities will be highlighted. As an illustration, we shall consider systems of different types of stochastic partial differential equation.