Electronic Journal of Probability

Competing super-Brownian motions as limits of interacting particle systems

Richard Durrett, Leonid Mytnik, and Edwin Perkins

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We study two-type branching random walks in which the birth or death rate of each type can depend on the number of neighbors of the opposite type. This competing species model contains variants of Durrett's predator-prey model and Durrett and Levin's colicin model as special cases. We verify in some cases convergence of scaling limits of these models to a pair of super-Brownian motions interacting through their collision local times, constructed by Evans and Perkins.

Article information

Electron. J. Probab., Volume 10 (2005), paper no. 35, 1147-1220.

Accepted: 9 September 2005
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G57: Random measures
Secondary: 60G17: Sample path properties

super-Brownian motion interacting branching particle systems collision local time competing species measure-valued diffusions

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Durrett, Richard; Mytnik, Leonid; Perkins, Edwin. Competing super-Brownian motions as limits of interacting particle systems. Electron. J. Probab. 10 (2005), paper no. 35, 1147--1220. doi:10.1214/EJP.v10-229. https://projecteuclid.org/euclid.ejp/1464816836

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