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May 2005 Rescaled Lotka–Volterra models converge to super-Brownian motion
J. Theodore Cox, Edwin A. Perkins
Ann. Probab. 33(3): 904-947 (May 2005). DOI: 10.1214/009117904000000973

Abstract

We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.

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J. Theodore Cox. Edwin A. Perkins. "Rescaled Lotka–Volterra models converge to super-Brownian motion." Ann. Probab. 33 (3) 904 - 947, May 2005. https://doi.org/10.1214/009117904000000973

Information

Published: May 2005
First available in Project Euclid: 6 May 2005

zbMATH: 1078.60082
MathSciNet: MR2135308
Digital Object Identifier: 10.1214/009117904000000973

Subjects:
Primary: 60G57 , 60K35
Secondary: 60F17 , 60J80

Keywords: coalescing random walk , Lotka–Volterra , spatial competition , Super-Brownian motion , voter model

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 3 • May 2005
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