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

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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.

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Authors
  1. G. Da Prato
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Additional information

Scuola Normale Superiore di Pisa, Italy. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 448–457, March, 1997.

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Da Prato, G. Regularity results for Kolmogorov equations in L 2 (H, μ) spaces and applications. Ukr Math J 49, 494–505 (1997). https://doi.org/10.1007/BF02487245

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  • DOI: https://doi.org/10.1007/BF02487245

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