2015-01-26Stochastic convective wave equation in two space dimensions
We briefly review stochastic partial differential equations driven by random source. We provide an overview of Walsh's stochastic integration with respect to martingale measure. We also study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing necessary and sufficient condition of Gaussian noise. Holder continuity of the solution is proved.