Geodesic
Nonlinear parabolic SPDEs involving Dirichlet operators
Tomasz Klimsiak 1   ; Andrzej Rozkosz 2
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland and Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
Studia Mathematica, Tome 230 (2015) no. 3, pp. 215-263 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8328-1-2016
Keywords: study problem existence uniqueness regularity probabilistic solutions cauchy problem nonlinear stochastic partial differential equations involving operators corresponding regular nonsymmetric dirichlet forms proofs combine methods backward doubly stochastic differential equations those probabilistic potential theory dirichlet forms

Tomasz Klimsiak  1   ; Andrzej Rozkosz  2

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland and Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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     title = {Nonlinear parabolic {SPDEs} involving {Dirichlet} operators},
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Tomasz Klimsiak; Andrzej Rozkosz. Nonlinear parabolic SPDEs involving Dirichlet operators. Studia Mathematica, Tome 230 (2015) no. 3, pp. 215-263. doi: 10.4064/sm8328-1-2016

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