ON THE ALMOST SURE BEHAVIOR OF SUMS OF IID RANDOM-VARIABLES IN HILBERT-SPACE

• 成果类型: Article
• 署名作者: EINMAHL, U
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990342
• 发表日期: 1991
• 页码: 1227-1263
• 关键词: banach-space; iterated logarithm; cluster set; lil; LAW

摘要

We study the almost sure behavior of sums of iid random variables satisfying the bounded LIL in Hilbert space. We show that the almost sure behavior is different from the Gaussian case, whenever the second strong moments are infinite. A law of the kappa times iterated logarithm is established which refines the bounded LIL. The interesting feature here is that contrary to the known conditions for the bounded LIL, one needs not only moment type conditions but also a nice structure of the covariance operator.