Large and moderate deviations for intersection local times

• 成果类型: Article
• 署名作者: Chen, X; Li, WV
• 署名单位: University of Tennessee System; University of Tennessee Knoxville; University of Delaware
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0298-7
• 发表日期: 2004
• 页码: 213-254
• 关键词: iterated logarithm; aleatory walks; CONVERGENCE; asymptotics; polymer; range; LAWS

摘要

We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L-2-norm of Brownian local times, and coincides with the large deviation obtained by Csorgo, Shi and Yor (1999) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results.