Bernoulli

  • Bernoulli
  • Volume 16, Number 4 (2010), 1343-1368.

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

Robert C. Dalang and Marta Sanz-Solé

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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.

Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 1343-1368.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092909

Digital Object Identifier
doi:10.3150/09-BEJ247

Mathematical Reviews number (MathSciNet)
MR2759182

Zentralblatt MATH identifier
1218.60054

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

Citation

Dalang, Robert C.; Sanz-Solé, Marta. Criteria for hitting probabilities with applications to systems of stochastic wave equations. Bernoulli 16 (2010), no. 4, 1343--1368. doi:10.3150/09-BEJ247. https://projecteuclid.org/euclid.bj/1290092909


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