Large deviations and laws of the iterated logarithm for the local times of additive stable processes

• 成果类型: Article
• 署名作者: Chen, Xia
• 署名单位: University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000601
• 发表日期: 2007
• 页码: 602-648
• 关键词: Levy processes; random-walks; brownian sheet; exponential asymptotics; capacity; points; sets

摘要

We study the upper tail behaviors of the local times of the additive stable processes. Let X-1 (t),..., X-p(t) be independent, d-dimensional symmetric stable processes with stable index 0 < alpha <= 2 and consider the additive stable process (X) over bar (t(1),..., t(p)) = X-1 (t(1)) + ... + X-p (t(p)). Under the condition d < alpha p, we obtain a precise form of the large deviation principle for the local time n(x)([0, t](p)) = integral(t)(o) ... integral(t)(o) delta(x)(X-1(s(1)) + ... + X-p (s(p))) ds(1) ... dsp of the multiparameter process (X) over bar (t(1),..., t(p)), and for its supremum norm SUPx is an element of Rd n(x)([0, t](p)). Our results apply to the law of the iterated logarithm and our approach is based on Fourier analysis, moment computation and time exponentiation.