Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||55 - 79|
|Published online||01 March 2007|
Infinite system of Brownian balls with interaction: the non-reversible case
Laboratoire CNRS 8524, UFR de Mathématiques,
Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France;
2 Institut für Mathematik, Universität Potsdam, Am Neuen Palais, 14415 Potsdam, Germany; firstname.lastname@example.org
3 On leave of absence Centre de Mathématiques Appliquées, UMR CNRS 7641, École Polytechnique, 91128 Palaiseau Cedex, France.
Accepted: September 2005
We consider an infinite system of hard balls in 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.
Mathematics Subject Classification: 60H10 / 60K35
Key words: Stochastic differential equation / local time / hard core potential / Gibbs measure / reversible measure.
© EDP Sciences, SMAI, 2007
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