Annals of Applied Probability

On collisions of Brownian particles

Tomoyuki Ichiba and Ioannis Karatzas

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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.

Article information

Ann. Appl. Probab., Volume 20, Number 3 (2010), 951-977.

First available in Project Euclid: 18 June 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G17: Sample path properties 60G44: Martingales with continuous parameter
Secondary: 60G85

Martingale problem triple collision effective dimension Bessel process reflected Brownian motion comparison theorem Atlas model


Ichiba, Tomoyuki; Karatzas, Ioannis. On collisions of Brownian particles. Ann. Appl. Probab. 20 (2010), no. 3, 951--977. doi:10.1214/09-AAP641.

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