Rescaled Lotka-Volterra models converge to super-Brownian motion

J. Theodore Cox, Edwin A. Perkins

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)904-947
Number of pages44
JournalAnnals of Probability
Volume33
Issue number3
DOIs
StatePublished - May 2005

Keywords

  • Coalescing random walk
  • Lotka-Volterra
  • Spatial competition
  • Super-Brownian motion
  • Voter model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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