Articlebronze2017

Multiple collisions in systems of competing Brownian particles

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Random Matrices and Applications

Abstract

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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References

1999Continuous Martingales and Brownian Motion 2008Stochastic differential equations and applications 1984Open Queueing Networks in Heavy Traffic 1981Reflected Brownian Motion on an Orthant 1987Brownian models of open queueing networks with homogeneous customer populations ∗1977A comparison theorem for solutions of stochastic differential equations and its applications 1998Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse 1987Multidimensional Reflected Brownian Motions Having Exponential Stationary Distributions

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