Existence of density for the stochastic wave equation with space-time homogeneous gaussian noise

© 2019, Institute of Mathematical Statistics. All rights reserved. In this article, we consider the stochastic wave equation on R+ × R, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions γ (in time) and f (in space), which are the Fourier transforms of tempered measures ν on R, respectively µ on R. Our main result shows that the law of the solution u(t, x) of this equation is absolutely continuous with respect to the Lebesgue measure.