Capture time of Brownian pursuits

• 成果类型: Article
• 署名作者: Li, WV; Shao, QM
• 署名单位: University of Delaware; University of Oregon
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008796
• 发表日期: 2001
• 页码: 30-48
• 关键词: exit times; motion; cones; maximum

摘要

Let B-0, B-1, ... , B-n be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time tau (n), = inf {t > 0 : B-i (t) - b(i) = B-0 (t) for some 1 less than or equal to i less than or equal to n} where 0 < b(i) less than or equal to 1, 1 < i less than or equal to n. In particular, we have E tau (3) = infinity and E tau (5) < infinity. Various generalizations are also studied.