Rescaled Lotka-Volterra models converge to super-Brownian motion

• 成果类型: Article
• 署名作者: Cox, JT; Perkins, EA
• 署名单位: Syracuse University; University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000973
• 发表日期: 2005
• 页码: 904-947
• 关键词: dimensions

摘要

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.