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.
Publié le : 2005-05-14
Classification:
Lotka–Volterra,
voter model,
super-Brownian motion,
spatial competition,
coalescing random walk,
60K35,
60G57,
60F17,
60J80
@article{1115386714,
author = {Cox, J. Theodore and Perkins, Edwin A.},
title = {Rescaled Lotka--Volterra models converge to super-Brownian motion},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 904-947},
language = {en},
url = {http://dml.mathdoc.fr/item/1115386714}
}
Cox, J. Theodore; Perkins, Edwin A. Rescaled Lotka–Volterra models converge to super-Brownian motion. Ann. Probab., Tome 33 (2005) no. 1, pp. 904-947. http://gdmltest.u-ga.fr/item/1115386714/