Sample path properties of parabolic SPDEs with non constant coefficients
arXiv:2410.23995 · doi:10.1007/s40072-025-00366-z
Abstract
We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path regularity of its solution.
28 pages