Interacting Brownian particles and Gibbs fields on pathspaces

David Dereudre

ESAIM: Probability and Statistics (2010)

  • Volume: 7, page 251-277
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Dereudre, David. "Interacting Brownian particles and Gibbs fields on pathspaces." ESAIM: Probability and Statistics 7 (2010): 251-277. <http://eudml.org/doc/104308>.

@article{Dereudre2010,
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. },
author = {Dereudre, David},
journal = {ESAIM: Probability and Statistics},
keywords = {Point measure on pathspace; Gibbs field; interacting Brownian particles; integration by parts formula; Campbell measure.; point measure on pathspace; interacting Brownian particles; Campbell measure},
language = {eng},
month = {3},
pages = {251-277},
publisher = {EDP Sciences},
title = {Interacting Brownian particles and Gibbs fields on pathspaces},
url = {http://eudml.org/doc/104308},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Dereudre, David
TI - Interacting Brownian particles and Gibbs fields on pathspaces
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 251
EP - 277
AB - 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.
LA - eng
KW - Point measure on pathspace; Gibbs field; interacting Brownian particles; integration by parts formula; Campbell measure.; point measure on pathspace; interacting Brownian particles; Campbell measure
UR - http://eudml.org/doc/104308
ER -

References

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