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Rescaled Lotka-Volterra models converge to super-Brownian motion

J. Theodore Cox·Edwin A. Perkins
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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. 2005-06-29. Rescaled Lotka-Volterra models converge to super-Brownian motion. https://doi.org/10.1214/009117904000000973

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