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A Gibbs variational principle in space-time for infinite-dimensional diffusions
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  • Published: February 2002

A Gibbs variational principle in space-time for infinite-dimensional diffusions

  • Paolo Dai Pra1,
  • Sylvie Roelly2 &
  • Hans Zessin3 

Probability Theory and Related Fields volume 122, pages 289–315 (2002)Cite this article

  • 108 Accesses

  • 8 Citations

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Abstract.

 We show that the set of stationary weak solutions for a class of infinite dimensional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata Università di Padova, Via Belzoni 7, 35131 Padova, Italy., , , , , , IT

    Paolo Dai Pra

  2. Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau Cedex, France., , , , , , FR

    Sylvie Roelly

  3. Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany, , , , , , DE

    Hans Zessin

Authors
  1. Paolo Dai Pra
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  2. Sylvie Roelly
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  3. Hans Zessin
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Additional information

Received: 20 May 1999 / Revised version: 14 May 2001 / Published online: 11 December 2001

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Pra, P., Roelly, S. & Zessin, H. A Gibbs variational principle in space-time for infinite-dimensional diffusions. Probab Theory Relat Fields 122, 289–315 (2002). https://doi.org/10.1007/s004400100170

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  • Issue Date: February 2002

  • DOI: https://doi.org/10.1007/s004400100170

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Keywords

  • Differential Equation
  • Weak Solution
  • Variational Principle
  • Stochastic Differential Equation
  • Gibbs Field
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