The multifractal spectrum of Brownian intersection local times

• 成果类型: Article
• 署名作者: Klenke, A; Mörters, P
• 署名单位: Johannes Gutenberg University of Mainz; University of Bath
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000116
• 发表日期: 2005
• 页码: 1255-1301
• 关键词: thick points; exponents; VALUES; EQUIVALENCE; motion; paths

摘要

Let f be the projected intersection local time of two independent Brownian paths in R-d for d = 2, 3. We determine the lower tail of the random variable l(U), where U is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.