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Singular dissipative stochastic equations in Hilbert spaces
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  • Published: October 2002

Singular dissipative stochastic equations in Hilbert spaces

  • Giuseppe Da Prato1 &
  • Michael Röckner2 

Probability Theory and Related Fields volume 124, pages 261–303 (2002)Cite this article

An Erratum to this article was published on 14 October 2008

Abstract.

 Existence of solutions to martingale problems corresponding to singular dissipative stochastic equations in Hilbert spaces are proved for any initial condition. The solutions for the single starting points form a conservative diffusion process whose transition semigroup is shown to be strong Feller. Uniqueness in a generalized sense is proved also, and a number of applications is presented.

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Authors and Affiliations

  1. Universität Bielefeld, Fak. Mathematik, Abt. Mathematik I, Universitätsstr. 25, D-33615 Bielefeld, Germany. e-mail:roeckner@mathematik.uni-bielefeld.de, , , , , , DE

    Giuseppe Da Prato

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy. e-mail:daprato@sns.it, , , , , , IT

    Michael Röckner

Authors
  1. Giuseppe Da Prato
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  2. Michael Röckner
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Additional information

Received: 14 November 2001 / Revised version: 8 April 2002 / Published online: 10 September 2002

An erratum to this article is available at http://dx.doi.org/10.1007/s00440-008-0179-1.

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Da Prato, G., Röckner, M. Singular dissipative stochastic equations in Hilbert spaces. Probab Theory Relat Fields 124, 261–303 (2002). https://doi.org/10.1007/s004400200214

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  • Issue Date: October 2002

  • DOI: https://doi.org/10.1007/s004400200214

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Keywords

  • Hilbert Space
  • Diffusion Process
  • Generalize Sense
  • Stochastic Equation
  • Transition Semigroup
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