Geodesic
Interacting brownian particles and Gibbs fields on pathspaces
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 251-277

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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.

DOI : 10.1051/ps:2003012
Classification : 60J60, 60K35, 60G55, 60G60, 82B21, 82C22
Keywords: point measure on pathspace, Gibbs field, interacting brownian particles, integration by parts formula, Campbell measure 
@article{PS_2003__7__251_0,
     author = {Dereudre, David},
     title = {Interacting brownian particles and {Gibbs} fields on pathspaces},
     journal = {ESAIM: Probability and Statistics},
     pages = {251--277},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     doi = {10.1051/ps:2003012},
     mrnumber = {1987789},
     zbl = {1038.60078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2003012/}
}
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Dereudre, David. Interacting brownian particles and Gibbs fields on pathspaces. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 251-277. doi: 10.1051/ps:2003012

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