Electronic Communications in Probability

Yet another condition for absence of collisions for competing Brownian particles

Tomoyuki Ichiba and Andrey Sarantsev

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Consider a finite system of rank-based competing Brownian particles, where the drift and diffusion of each particle depend only on its current rank relative to other particles. We present a simple sufficient condition for absence of multiple collisions of a given order, continuing the earlier work by Bruggeman and Sarantsev (2015). Unlike in that paper, this new condition works even for infinite systems.

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Electron. Commun. Probab., Volume 22 (2017), paper no. 8, 7 pp.

Received: 25 August 2016
Accepted: 2 January 2017
First available in Project Euclid: 14 January 2017

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H10: Stochastic ordinary differential equations [See also 34F05] 60J65: Brownian motion [See also 58J65] 60J60: Diffusion processes [See also 58J65]

competing Brownian particles total collision multiple collision triple collision simultaneous collision

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Ichiba, Tomoyuki; Sarantsev, Andrey. Yet another condition for absence of collisions for competing Brownian particles. Electron. Commun. Probab. 22 (2017), paper no. 8, 7 pp. doi:10.1214/17-ECP41. https://projecteuclid.org/euclid.ecp/1484363135

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