Interacting Brownian particles and Gibbs fields on pathspaces
Centre de Mathématiques Appliquées,
UMR 7641, École Polytechnique, 91128 Palaiseau Cedex, France; email@example.com.
Revised: 29 January 2003
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.
Mathematics Subject Classification: 60J60 / 60K35 / 60G55 / 60G60 / 82B21 / 82C22
Key words: Point measure on pathspace / Gibbs field / interacting Brownian particles / integration by parts formula / Campbell measure.
© EDP Sciences, SMAI, 2003