SINGULARITY OF SUPER-BROWNIAN LOCAL, TIME AT A POINT CATALYST

• 成果类型: Article
• 署名作者: DAWSON, DA; FLEISCHMANN, K; LI, Y; MUELLER, C
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Rochester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988375
• 发表日期: 1995
• 页码: 37-55
• 关键词: partial-differential equations; superprocesses

摘要

In a one-dimensional single point-catalytic continuous super-Brownian motion studied by Dawson and Fleischmann, the occupation density measure lambda(c) at the catalyst's position C is shown to be a singular (diffuse) random measure. The source of this qualitative new effect is the irregularity of the varying medium delta(c) describing the point catalyst. The proof is based on a probabilistic characterization of the law of the Palm canonical clusters chi appearing in the Levy-Khintchine representation of lambda(c) in a historical process setting and the fact that these chi have infinite left upper density (with respect to Lebesgue measure) at the Palm time point.