Some criteria for hitting probabilities. Application to systems of stochastic wave equation with additive noise

Some criteria for hitting probabilities. Application to systems of stochastic wave equation with additive noise

Mon, 02/03/2009
14:15 		Professor Marta Sanz Solé (Universitat de Barcelona) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Some criteria for hitting probabilities. Application to systems of stochastic wave equation with additive noise
We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k≥1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and coloured in space.