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Some properties of invariant measures of non symmetric dissipative stochastic systems
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  • Published: July 2002

Some properties of invariant measures of non symmetric dissipative stochastic systems

  • Giuseppe Da Prato1,
  • Arnaud Debussche2 &
  • Beniamin Goldys3 

Probability Theory and Related Fields volume 123, pages 355–380 (2002)Cite this article

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Abstract.

 We consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms. We prove an integration by part formula and a Logarithmic Sobolev inequality for the invariant measure. No symmetry or reversibility assumptions are made. Furthemore we prove some compactness results on the transition semigroup and on the embedding of the Sobolev spaces based on the invariant measure. We use these results to derive asymptotic properties for a stochastic reaction–diffusion equation.

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Authors and Affiliations

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

    Giuseppe Da Prato

  2. Ecole Normale Supérieure de Cachan, antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France, , , , , , FR

    Arnaud Debussche

  3. School of Mathematics, The University of New South Wales Sydney 2052, Australia, , , , , , AU

    Beniamin Goldys

Authors
  1. Giuseppe Da Prato
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  2. Arnaud Debussche
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  3. Beniamin Goldys
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Additional information

Received: 29 September 2000 / Revised version: 30 May 2001 / Published online: 14 June 2002

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Da Prato, G., Debussche, A. & Goldys, B. Some properties of invariant measures of non symmetric dissipative stochastic systems. Probab Theory Relat Fields 123, 355–380 (2002). https://doi.org/10.1007/s004400100188

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  • Issue Date: July 2002

  • DOI: https://doi.org/10.1007/s004400100188

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Sobolev Space
  • Invariant Measure
  • Diffusion Equation
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