Nonlinear parabolic SPDEs involving Dirichlet operators

Tomasz Klimsiak, Andrzej Rozkosz

Published 2016-04-25Version 1

We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving operators corresponding to regular (nonsymmetric) Dirichlet forms. In proofs we combine the methods of backward doubly stochastic differential equations with those of probabilistic potential theory and Dirichlet forms.