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Infinite system of Brownian balls with interaction: the non-reversible case

Published online by Cambridge University Press:  01 March 2007

Myriam Fradon  and
Sylvie Rœlly
Myriam Fradon
Affiliation:
Laboratoire CNRS 8524, UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France; Myriam.Fradon@univ-lille1.fr
Sylvie Rœlly
Affiliation:
Institut für Mathematik, Universität Potsdam, Am Neuen Palais, 14415 Potsdam, Germany; roelly@math.uni-potsdam.de On leave of absence Centre de Mathématiques Appliquées, UMR CNRS 7641, École Polytechnique, 91128 Palaiseau Cedex, France.
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Abstract

We consider an infinite system of hard balls in $\xR^d$ undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.

Keywords

Stochastic differential equationlocal timehard core potentialGibbs measurereversible measure.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 55 - 79
Copyright
© EDP Sciences, SMAI, 2007

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References

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