Electronic Journal of Probability

Regularizing Properties for Transition Semigroups and Semilinear Parabolic Equations in Banach Spaces

Federica Masiero

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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 $E$.

Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 13, 387-419.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464818484

Digital Object Identifier
doi:10.1214/EJP.v12-401

Mathematical Reviews number (MathSciNet)
MR2299922

Zentralblatt MATH identifier
1127.60065

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60G15: Gaussian processes

Keywords
Ornstein-Uhlenbeck and perturbed Ornstein-Uhlenbeck transition semigroups regularizing properties parabolic equations Banach spaces

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Masiero, Federica. Regularizing Properties for Transition Semigroups and Semilinear Parabolic Equations in Banach Spaces. Electron. J. Probab. 12 (2007), paper no. 13, 387--419. doi:10.1214/EJP.v12-401. https://projecteuclid.org/euclid.ejp/1464818484


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