THE PACKING MEASURE OF THE RANGE OF SUPER-BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Duquesne, Thomas
• 署名单位: Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP468
• 发表日期: 2009
• 页码: 2431-2458
• 关键词: random tree

摘要

We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r) = r(4)(log log l/r)(-3) in super-critical dimensions d >= 5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.