Displaying similar documents to “Regularizing properties for transition semigroups and semilinear parabolic equations in Banach spaces.”

Regularity results for infinite dimensional diffusions. A Malliavin calculus approach

Stefano Bonaccorsi, Marco Fuhrman (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove some smoothing properties for the transition semigroup associated to a nonlinear stochastic equation in a Hilbert space. The proof introduces some tools from the Malliavin calculus and is based on a integration by parts formula.

Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation

Giuseppe Da Prato, Arnaud Debussche (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup P t ⁢ φ does exist for any bounded φ ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.

Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

Zdzisław Brzeźniak, Szymon Peszat (1999)

Studia Mathematica

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Stochastic partial differential equations on ℝ d are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted L q -space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.