## Electronic Journal of Probability

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

Federica Masiero

#### 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

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

Rights

#### 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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