On collisions of Brownian particles

Details On collisions of Brownian particles On collisions of Brownian particles

2008-10-13

arxiv.org/abs/0810.2149v3

Annals of Applied Probability 2010, Vol. 20, No. 3, 951-977

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP641 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP641

We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient conditions are established for the absence and for the presence of triple collisions among the particles. As an application to the Atlas model for equity markets, we study a special construction of such systems of diffusing particles using Brownian motions with reflection on polyhedral domains.

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