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Interacting Brownian particles and Gibbs fields on pathspaces

Published online by Cambridge University Press:  15 May 2003

David Dereudre
David Dereudre*
Affiliation:
Centre de Mathématiques Appliquées, UMR 7641, École Polytechnique, 91128 Palaiseau Cedex, France; dereudre@cmapx.polytechnique.fr.
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Abstract

In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Keywords

Point measure on pathspaceGibbs fieldinteracting Brownian particlesintegration by parts formulaCampbell measure.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 251 - 277
Copyright
© EDP Sciences, SMAI, 2003

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