Interacting brownian particles and Gibbs fields on pathspaces

Dereudre, David

ESAIM: Probability and Statistics, Tome 7 (2003), pp. 251-277.

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.

Classification : 60J60, 60K35, 60G55, 60G60, 82B21, 82C22
Mots clés : point measure on pathspace, Gibbs field, interacting brownian particles, integration by parts formula, Campbell measure

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