| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 55 - 79 | |
| DOI | https://doi.org/10.1051/ps:2007006 | |
| Published online | 01 March 2007 | |
Infinite system of Brownian balls with interaction: the non-reversible case
1
Laboratoire CNRS 8524, UFR de Mathématiques,
Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France;
Myriam.Fradon@univ-lille1.fr
2
Institut für Mathematik, Universität Potsdam, Am Neuen Palais,
14415 Potsdam, Germany;
roelly@math.uni-potsdam.de
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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