Strong clumping of super-Brownian motion in a stable catalytic medium

• 成果类型: Article
• 署名作者: Dawson, DA; Fleischmann, K; Mörters, P
• 署名单位: Carleton University; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1990-2045
• 关键词: valued branching-processes; anderson model; superprocesses; support

摘要

A typical feature of the long time behavior of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We describe this phenomenon by means of a functional limit theorem under renormalization. The limiting process is a Poisson point field of mass clumps with no spatial motion component and with infinite variance. The mass of each cluster evolves independently according to a non-Markovian continuous process trapped at mass zero, which we describe explicitly by means of a Brownian snake construction in a random medium. We also determine the survival probability and asymptotic size of the clumps.