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. |