The Annals of Applied Probability

On collisions of Brownian particles

Tomoyuki Ichiba and Ioannis Karatzas

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Abstract

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

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

Dates
First available in Project Euclid: 18 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1276867303

Digital Object Identifier
doi:10.1214/09-AAP641

Mathematical Reviews number (MathSciNet)
MR2680554

Zentralblatt MATH identifier
1235.60111

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

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

Citation

Ichiba, Tomoyuki; Karatzas, Ioannis. On collisions of Brownian particles. Ann. Appl. Probab. 20 (2010), no. 3, 951--977. doi:10.1214/09-AAP641. https://projecteuclid.org/euclid.aoap/1276867303


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