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INFINITELY MANY BROWNIAN GLOBULES WITH BROWNIAN RADII

UMR CNRS 8524, UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France

and

Institut für Mathematik der Universität Potsdam, Am Neuen Palais, 10, 14469 Potsdam, Germany

On leave of absence from Centre de Mathématiques Appliquées, UMR C.N.R.S. 7641, École Polytechnique, 91128 Palaiseau Cedex, France.

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https://doi.org/10.1142/S021949371000311XCited by:3 (Source: Crossref)

Abstract

We consider an infinite system of non-overlapping globules undergoing Brownian motions in ℝ³. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.

Keywords:

AMSC: 60H10, 60J55, 60J60

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