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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8328-1-2016,
author = {Tomasz Klimsiak and Andrzej Rozkosz},
title = {Nonlinear parabolic SPDEs involving Dirichlet operators},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {215-263},
zbl = {06545405},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8328-1-2016}
}
Tomasz Klimsiak; Andrzej Rozkosz. Nonlinear parabolic SPDEs involving Dirichlet operators. Studia Mathematica, Tome 231 (2015) pp. 215-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8328-1-2016/