(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
Wilhelm Stannat (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Displaying similar documents to “Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization”
(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.
Niels Jacob (1993)
Revista Matemática Iberoamericana
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We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.
Dirichlet problem for a linear elliptic equation in unbounded domains with -boundary data
J. Chabrowski (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Nonlinear parabolic SPDEs involving Dirichlet operators
Tomasz Klimsiak, Andrzej Rozkosz (2015)
Studia Mathematica
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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.
Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms
Tomasz Klimsiak, Andrzej Rozkosz (2016)
Colloquium Mathematicae
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We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with...
-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
Vitali Liskevich, Michael Röckner, Zeev Sobol, Oleksiy Us (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Some Dirichlet spaces obtained by subordinate reflected diffusions.
Niels Jacob, René L. Schilling (1999)
Revista Matemática Iberoamericana
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In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
The Dirichlet problem in half-space for elliptic equations with unbounded coefficients
J. H. Chabrowski (1987)
Rendiconti del Seminario Matematico della Università di Padova
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Stochastic representation of reflecting diffusions corresponding to divergence form operators
Andrzej Rozkosz, Leszek Słomiński (2000)
Studia Mathematica
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We obtain a stochastic representation of a diffusion corresponding to a uniformly elliptic divergence form operator with co-normal reflection at the boundary of a bounded -domain. We also show that the diffusion is a Dirichlet process for each starting point inside the domain.