Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 20, Number 3 (2010), 951-977.
On collisions of Brownian particles
Tomoyuki Ichiba and Ioannis Karatzas
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