SOME EXTENSIONS OF THE LIL VIA SELF-NORMALIZATIONS

• 成果类型: Article
• 署名作者: GRIFFIN, P; KUELBS, J
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990551
• 发表日期: 1991
• 页码: 380-395
• 关键词: iterated logarithm; THEOREM; sums

摘要

We study some generalizations of the LIL when self-normalizations are used. Two particular results proved are: (1) an extension of the Kolmogorov-Erdos test for partial sums of symmetric i.i.d. random variables having finite second moments; this result eliminates distinctions required when nonrandom normalizers are used and E(X2I(\X\ > t)) is not O((L2t)-1), and (2) an extension of a universal bounded LIL of Marcinkiewicz to nonsymmetric random variables. An interesting corollary of this work is a short new proof of the classical LIL avoiding truncation methods.