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November 2010 Criteria for hitting probabilities with applications to systems of stochastic wave equations
Robert C. Dalang, Marta Sanz-Solé
Bernoulli 16(4): 1343-1368 (November 2010). DOI: 10.3150/09-BEJ247

Abstract

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 colored in space.

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Robert C. Dalang. Marta Sanz-Solé. "Criteria for hitting probabilities with applications to systems of stochastic wave equations." Bernoulli 16 (4) 1343 - 1368, November 2010. https://doi.org/10.3150/09-BEJ247

Information

Published: November 2010
First available in Project Euclid: 18 November 2010

zbMATH: 1218.60054
MathSciNet: MR2759182
Digital Object Identifier: 10.3150/09-BEJ247

Keywords: capacity , Hausdorff measure , hitting probabilities , spatially homogeneous colored noise , systems of stochastic wave equations

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 4 • November 2010
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