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2007 Regularizing Properties for Transition Semigroups and Semilinear Parabolic Equations in Banach Spaces
Federica Masiero
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Electron. J. Probab. 12: 387-419 (2007). DOI: 10.1214/EJP.v12-401

Abstract

We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space $E$ which is continuously and densely embedded in a real and separable Hilbert space $H$. Namely we study conditions under which the transition semigroup maps continuous and bounded functions into differentiable functions. Via a Girsanov type theorem such properties extend to perturbed Ornstein Uhlenbeck processes. We apply the results to solve in mild sense semilinear versions of Kolmogorov equations in $E$.

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Federica Masiero. "Regularizing Properties for Transition Semigroups and Semilinear Parabolic Equations in Banach Spaces." Electron. J. Probab. 12 387 - 419, 2007. https://doi.org/10.1214/EJP.v12-401

Information

Accepted: 7 April 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60065
MathSciNet: MR2299922
Digital Object Identifier: 10.1214/EJP.v12-401

Subjects:
Primary: 60H30
Secondary: 60G15 , 60H07

Keywords: ‎Banach spaces , Ornstein-Uhlenbeck and perturbed Ornstein-Uhlenbeck transition semigroups , Parabolic equations , regularizing properties

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Vol.12 • 2007
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