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.

Masiero, F. (2007). Regularizing properties for transition semigroups and semilinear parabolic equations in Banach spaces. ELECTRONIC JOURNAL OF PROBABILITY, 12, 387-419 [10.1214/EJP.v12-401].

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

MASIERO, FEDERICA
2007

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.
Articolo in rivista - Articolo scientifico
Ornstein-Uhlenbeck and perturbed Ornstein-Uhlenbeck transition semigroups; regularizing properties; parabolic equations; Banach spaces
English
7-apr-2007
12
387
419
none
Masiero, F. (2007). Regularizing properties for transition semigroups and semilinear parabolic equations in Banach spaces. ELECTRONIC JOURNAL OF PROBABILITY, 12, 387-419 [10.1214/EJP.v12-401].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/268
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