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A Gibbs variational principle in space-time for infinite-dimensional diffusions |
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| Authors: | Paolo Dai Pra Sylvie Roelly Hans Zessin |
| Institution: | Dipartimento di Matematica Pura e Applicata Università di Padova, Via Belzoni 7, 35131 Padova, Italy., IT Centre de Mathématiques Appliquées, école Polytechnique, 91128 Palaiseau Cedex, France., FR Fakult?t für Mathematik, Universit?t Bielefeld, 33501 Bielefeld, Germany, DE |
| 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. Received: 20 May 1999 / Revised version: 14 May 2001 / Published online: 11 December 2001 |
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