The exact packing measure of Brownian double points

• 成果类型: Article
• 署名作者: Morters, Peter; Shieh, Narn-Rueih
• 署名单位: University of Bath; National Taiwan University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0122-x
• 发表日期: 2009
• 页码: 113-136
• 关键词: intersection local-times; plane exponents; VALUES; path

摘要

Let D subset of R-3 be the set of double points of a three-dimensional Brownian motion. We show that, if xi = xi 3(2, 2) is the intersection exponent of two packets of two independent Brownian motions, then almost surely, the phi-packing measure of D is zero if integral(0+) r(-1-xi)phi(r)(xi) dr < infinity, and infinity otherwise. As an important step in the proof we show up-to-constants estimates for the tail at zero of Brownian intersection local times in dimensions two and three.