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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 13 open journal systems 


Regularizing properties for transition semigroups and semilinear parabolic equations in Banach spaces

Federica Masiero, Universita di Milano-Bicocca


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.


Full text: PDF

Pages: 387-419

Published on: April 7, 2007
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Electronic Journal of Probability. ISSN: 1083-6489