Open Access
February 2018 Multiple collisions in systems of competing Brownian particles
Cameron Bruggeman, Andrey Sarantsev
Bernoulli 24(1): 156-201 (February 2018). DOI: 10.3150/16-BEJ869


Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a sufficient condition for a.s. absence of a total collision (when all particles collide) and of other types of collisions, say of the three lowest-ranked particles. This continues the work of Ichiba, Karatzas and Shkolnikov [Probab. Theory Related Fields 156 (2013) 229–248] and Sarantsev (2016).


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Cameron Bruggeman. Andrey Sarantsev. "Multiple collisions in systems of competing Brownian particles." Bernoulli 24 (1) 156 - 201, February 2018.


Received: 1 September 2015; Revised: 1 May 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778324
MathSciNet: MR3706753
Digital Object Identifier: 10.3150/16-BEJ869

Keywords: Asymmetric collisions , Competing Brownian particles , multiple collisions , named particles , positive orthant , ranked particles , reflected Brownian motion , Skorohod problem , squared Bessel process , Stochastic comparison , Triple collisions

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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