Ukrainian Mathematical Journal

, Volume 49, Issue 3, pp 494–505 | Cite as

Regularity results for Kolmogorov equations in L 2 (H, μ) spaces and applications

  • G. Da Prato
Article

Abstract

We consider the transition semigroup R t =e tsA associated to an Ornstein—Uhlenbeck process in a Hilbert space H. We characterize, under suitable assumptions, the domain of A as a subspace W2,2 (H, μ), where μ is the invariant measure associated to R t . This characterization is then used to treat some Kolmogorov equations with variable coefficients.

Keywords

Linear Operator Invariant Measure Regularity Result Dirichlet Form Separable Hilbert Space 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • G. Da Prato

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