Solving the hyperbolic Anderson model 1: Skorohod setting

Abstract

This paper is concerned with a wave equation in dimension $d\in \{1,2,3\}$, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the space-time covariance of the Gaussian noise, allowing the existence and uniqueness of a mild Skorohod solution.