Nonlinear parabolic SPDEs involving Dirichlet operators

Tomasz Klimsiak, and Andrzej Rozkosz. "Nonlinear parabolic SPDEs involving Dirichlet operators." Studia Mathematica 230.3 (2015): 215-263. <http://eudml.org/doc/285656>.

@article{TomaszKlimsiak2015,
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.},
author = {Tomasz Klimsiak, Andrzej Rozkosz},
journal = {Studia Mathematica},
keywords = {stochastic partial differential equation; backward doubly stochastic differential equation; Dirichlet form},
language = {eng},
number = {3},
pages = {215-263},
title = {Nonlinear parabolic SPDEs involving Dirichlet operators},
url = {http://eudml.org/doc/285656},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Tomasz Klimsiak
AU - Andrzej Rozkosz
TI - Nonlinear parabolic SPDEs involving Dirichlet operators
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 3
SP - 215
EP - 263
AB - 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.
LA - eng
KW - stochastic partial differential equation; backward doubly stochastic differential equation; Dirichlet form
UR - http://eudml.org/doc/285656
ER -