Rescaled Lotka-Volterra models converge to super-Brownian motion
Probability
2007-05-23 v1
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.
Cite
@article{arxiv.math/0506591,
title = {Rescaled Lotka-Volterra models converge to super-Brownian motion},
author = {J. Theodore Cox and Edwin A. Perkins},
journal= {arXiv preprint arXiv:math/0506591},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117904000000973 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)