Revista Matemática Iberoamericana


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Volume 30, Issue 2, 2014, pp. 685–709
DOI: 10.4171/RMI/796

Published online: 2014-07-08

Hitting times for the stochastic wave equation with fractional colored noise

Jorge Clarke de la Cerda[1] and Ciprian A. Tudor[2]

(1) Universidad del Bío-Bío, Concepción, Chile
(2) CNRS-Université Lille I, Villeneuve d'Ascq, France

We give sharp regularity results for the solution to the stochastic wave equation with linear fractional-colored noise. We apply these results in order to establish upper and lower bounds for the hitting probabilities of the solution in terms of the Hausdorff measure and the Newtonian capacity.

Keywords: Stochastic wave equation, potential theory, hitting probability, capacity, Hausdorff dimension, spatially homogeneous Gaussian noise, fractional Brownian motion, H

Clarke de la Cerda Jorge, Tudor Ciprian: Hitting times for the stochastic wave equation with fractional colored noise. Rev. Mat. Iberoamericana 30 (2014), 685-709. doi: 10.4171/RMI/796