# Lluís Quer-Sardanyons: The Hyperbolic Anderson Model with rough noise in space

Lluís Quer-Sardanyons (Universitat Autònoma de Barcelona) gives a lecture with the title: The Hyperbolic Anderson Model with rough noise in space

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 1/4<H<1/2 . 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 of the solution, for any p\geq 2. The condition H>1/4 turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one interpreted in the Itô sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent.

The talk is based on a joint work with Raluca Balan (Univ. of Ottawa) and Maria Jolis (Autonomous Univ. of Barcelona).