Rescaled Lotka–Volterra models converge to super-Brownian motion

2005/05/01 by J. Theodore Cox, Edwin A. Perkins · 1 citation
Economics, Econometrics and Finance · Mathematics · #COVID-19 epidemiological studies #Point processes and geometric inequalities #Spatial and Panel Data Analysis #math.PR

paper · pdf · doi:10.1214/009117904000000973

published as Annals of Probability 2005, Vol. 33, No. 3, 904-947 · 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)

openalex publication_date 2005/05/01 · arxiv created 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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