Tomoyuki Ichiba, Ioannis Karatzas
Published 2008-10-13, updated 2010-10-18Version 3
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.
Comments: Published in at http://dx.doi.org/10.1214/09-AAP641 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2010, Vol. 20, No. 3, 951-977
Coalescence on the real line
Non-colliding system of Brownian particles as Pfaffian process
Poisson statistics for beta ensembles on the real line at high temperature
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