Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 8, 7 pp.
Yet another condition for absence of collisions for competing Brownian particles
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.
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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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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