Thick points of super-Brownian motion

• 成果类型: Article
• 署名作者: Blath, J; Mörters, P
• 署名单位: University of Oxford; University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0387-2
• 发表日期: 2005
• 页码: 604-630
• 关键词: multifractal structure; local-times; dimension; trees

摘要

We determine for a super-Brownian motion {X-t : t >= 0} in R-d, d >= 3, the precise gauge function phi such that, almost surely on survival up to time t, [GRAPHICS] improving a result of Barlow, Evans and Perkins about the most visited sites of super-Brownian motion. We also determine upper and lower bounds for the Hausdorff dimension spectrum of thick points refining the multifractal analysis of super-Brownian motion by Taylor and Perkins. The upper bound, conjectured to be sharp, involves a constant which can be characterized in terms of the upper tails of the associated equilibrium Palm distribution.