RATES OF CLUSTERING IN STRASSENS LIL FOR PARTIAL SUM PROCESSES

• 成果类型: Article
• 署名作者: EINMAHL, U; MASON, DM
• 署名单位: University of Delaware
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01192960
• 发表日期: 1993
• 页码: 479-487
• 关键词: iterated logarithm; CONVERGENCE; LAWS

摘要

We provide a detailed description of the rate of clustering in Strassen's functional law of the iterated logarithm for partial sum processes. Necessary and sufficient conditions are given for certain clustering rates in terms of moment-type conditions. In the process, we also derive a new strong approximation of sums of iid random variables by a Wiener process.