Criteria for hitting probabilities with applications to systems of stochastic wave equations

Details Criteria for hitting probabilities with applications to systems of stochastic wave equations Criteria for hitting probabilities with applications to systems of stochastic wave equations

2009-02-26

arxiv.org/abs/0902.4583v2

Bernoulli 2010, Vol. 16, No. 4, 1343-1368

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/09-BEJ247 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ247

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 $k\ge1$ driven by a $d$-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

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