Intermittency for the Hyperbolic Anderson Model with rough noise in space

© 2016 Elsevier B.V. In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index H∈([Formula presented], [Formula presented]). Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the p-th moment the solution, for any p≥2. Condition H>[Formula presented] turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one obtained by the authors in a recent publication, in which the solution is interpreted in the Itô sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent.