A functional LIL for symmetric stable processes

• 成果类型: Article
• 署名作者: Chen, X; Kuelbs, J; Li, WB
• 署名单位: Northwestern University; University of Wisconsin System; University of Wisconsin Madison; University of Delaware
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 258-276
• 关键词: iterated logarithm; LAWS

摘要

A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion. Proofs depend on small ball probability estimates and yield the small ball probabilities of the weighted sup-norm for these processes.