Lluís Quer-Sardanyons, Universitat Autònoma Barcelona

Existence of Density for the Stochastic Wave Equation with Space-time Homogeneous Noise

Abstract

We consider the stochastic wave equation in spatial dimension one or two, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structure are given by locally integrable functions, which are the Fourier transforms of tempered measures. The main result shows that the law of the solution of this equation is absolutely continuous with respect to the Lebesgue measure, provided that the spatial spectral measure satisfies an integrability condition which ensures that the sample paths of the solution are Hölder continuous.