STRONG LIMIT-THEOREMS FOR LARGE AND SMALL INCREMENTS OF L(P)-VALUED GAUSSIAN-PROCESSES

• 成果类型: Article
• 署名作者: CSORGO, M; SHAO, QM
• 署名单位: Zhejiang University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989007
• 发表日期: 1993
• 页码: 1958-1990
• 关键词: ornstein-uhlenbeck processes; continuity; inequalities; REGULARITY; MODULI; wiener

摘要

Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for l(p)-valued, 1 less than or equal to p < infinity, Gaussian processes with stationary increments. Applications to l(p)-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refine and extend those of Csaki, Csorgo and Shao.