Moment bounds and asymptotics for the stochastic wave equation

Abstract

We consider the stochastic wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to obtain sharp bounds on growth indices for certain classes of initial conditions with unbounded support. (C) 2014 Elsevier B.V. All rights reserved.PRO