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.
Publié le : 2010-11-15
Classification:
capacity,
Hausdorff measure,
hitting probabilities,
spatially homogeneous colored noise,
systems of stochastic wave equations
@article{1290092909,
author = {Dalang, Robert C. and Sanz-Sol\'e, Marta},
title = {Criteria for hitting probabilities with applications to systems of stochastic wave equations},
journal = {Bernoulli},
volume = {16},
number = {1},
year = {2010},
pages = { 1343-1368},
language = {en},
url = {http://dml.mathdoc.fr/item/1290092909}
}
Dalang, Robert C.; Sanz-Solé, Marta. Criteria for hitting probabilities with applications to systems of stochastic wave equations. Bernoulli, Tome 16 (2010) no. 1, pp. 1343-1368. http://gdmltest.u-ga.fr/item/1290092909/