Sanz-Solé, Marta; Matematični kolokvij Februar 2012

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Deterministic sets visited by random trajectories

Marta Sanz-Solé

Universitat de Barcelona

16. februar 2012

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.

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