The small-time Chung-Wichura law for Levy processes with non-vanishing Brownian component

• 成果类型: Article
• 署名作者: Buchmann, Boris; Maller, Ross
• 署名单位: Monash University; Australian National University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0255-1
• 发表日期: 2011
• 页码: 303-330
• 关键词: small ball probabilities; functional lil; strassen

摘要

We give a small time functional version of Chung's other law of the iterated logarithm for L,vy processes with non-vanishing Brownian component. This is an analogue of the other law of the iterated logarithm at large times for L,vy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.