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Regularity of invariant measures for a class of perturbed Ornstein-Uhlenbeck operators

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Abstract

In the framework of [5] we prove regularity of invariant measures μ for a class of Ornstein-Uhlenbeck operators perturbed by a drift which is not necessarily bounded or Lipschitz continuous. Regularity here means that μ is absolutely continuous with respect to the Gaussian invariant measure of the unperturbed operator with the square root of the Radon-Nikodym density in the corresponding Sobolev space of order 1.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia

    Vladimir I. Bogachev

  2. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 6, 56126, Pisa, Italy

    Giuseppe Da Prato

  3. Faculty of Mathematics, University of Bielefeld, D-33615, Bielefeld, Germany

    Michael Röckner

Authors
  1. Vladimir I. Bogachev
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  2. Giuseppe Da Prato
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  3. Michael Röckner
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Additional information

Partially supported by the International Science Foundation (Grant M 38000), the Russian Foundation of Fundamental Research (Grant 94-01-01556), and EC-Science Project SC1*CT92-0784.

Partially supported by the Italian National Project MURST “Problemi nonlineari nell'Analisi”

Partially supported by the DFG(SFB-256-Bonn, SFB-343-Bielefeld) and EC-Science Project SC1*CT92-0784.

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Bogachev, V.I., Da Prato, G. & Röckner, M. Regularity of invariant measures for a class of perturbed Ornstein-Uhlenbeck operators. NoDEA 3, 261–268 (1996). https://doi.org/10.1007/BF01195918

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  • DOI: https://doi.org/10.1007/BF01195918

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