Rescaled Lotka-Volterra models converge to super-Brownian motion

Details Rescaled Lotka-Volterra models converge to super-Brownian motion Rescaled Lotka-Volterra models converge to super-Brownian motion

2005-06-29

arxiv.org/abs/math/0506591v1

Annals of Probability 2005, Vol. 33, No. 3, 904-947

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000973 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000973

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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