Stochastic partial differential equations driven by colored noise

Abstract

This dissertation studies some problems for stochastic partial differential equations, in particular, (nonlinear) stochastic heat and stochastic wave equations, driven by (multiplicative) colored Gaussian noises. These problems considered are existence and uniqueness of the solution, Hölder continuity of the solution, Feynman-Kac formula for the solution, Feynman-Kac formula for the moments of the solution, Smoothness of the density of the solution as a random vectors at different spatial locations, intermittency (asymptotics for the high moments of the solution).