LARGE DEVIATIONS FOR LOCAL TIMES AND INTERSECTION LOCAL TIMES OF FRACTIONAL BROWNIAN MOTIONS AND RIEMANN-LIOUVILLE PROCESSES

• 成果类型: Article
• 署名作者: Chen, Xia; Li, Wenbo V.; Rosinski, Jan; Shao, Qi-Man
• 署名单位: University of Tennessee System; University of Tennessee Knoxville; University of Delaware; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP566
• 发表日期: 2011
• 页码: 729-778
• 关键词: small ball probabilities; random-walk; iterated logarithm; Moderate Deviations; asymptotics; LAW

摘要

In this paper, we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.