A cyclically catalytic super-Brownian motion

• 成果类型: Article
• 署名作者: Fleischmann, K; Xiong, J
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1008956694
• 发表日期: 2001
• 页码: 820-861
• 关键词: particle-systems; branching model; time behavior; COMPETITION; equation

摘要

In generalization of the mutually catalytic super-Brownian motion in R of Dawson and Perkins and Mytnik, a function-valued cyclically catalytic model X is constructed as a strong Markov solution to a martingale problem. Starting with a finite population X-0, each pair of neighboring types will globally segregate in the long-term limit (noncoexistence of neighboring types). Also finer extinction-survival properties depending on X-0 are studied in the spirit of Mueller and Perkins. In fact, X-0 can be chosen in such a way that all types survive for all finite times. On the other hand, sufficient conditions on X-0 are stated for the following situation: given a type k and a positive time t, the kth subpopulation X-k dies by time t with a large probability, provided that its initial value X-0(k) was sufficiently small.