Sample path regularity of non-autonomous uniformly parabolic SPDEs

Abstract

We consider a stochastic PDE driven by a parabolic second order partial differential operator with non-constant coefficients and with a nonlinear random external forcing given by a Gaussian noise that is white in time and spatially homogeneous. We prove the existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path Hölder-continuity properties of the solution. The Hölder exponents that we obtain are essentially optimal.