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Interacting Brownian particles and Gibbs fields on pathspaces
David Dereudre
Journal:

ESAIM: Probability and Statistics / Volume 7 / March 2003

Published online by Cambridge University Press:

15 May 2003, pp. 251-277

Print publication:

March 2003
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In this paper, we prove that the laws of interacting Brownian particlesare characterized as Gibbs fields on pathspace associated to an explicit class ofHamiltonian functionals. More generally, we show that a large class of Gibbsfields on pathspace corresponds to Brownian diffusions. Some applications totime reversal in the stationary and non stationary case are presented.