Nonlinear parabolic SPDEs involving Dirichlet operators
Volume 230 / 2015
Studia Mathematica 230 (2015), 215-263
MSC: Primary 60H15; Secondary 60H10, 60H30, 35R60.
DOI: 10.4064/sm8328-1-2016
Published online: 8 February 2016
Abstract
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 the proofs we combine the methods of backward doubly stochastic differential equations with those of probabilistic potential theory and Dirichlet forms.
