在最少条件下的对数律精确渐近性

Precise Rates in the Law of the Logarithm under Minimal Conditions

摘要: 设X_1,X_2,\cdots为独立同分布随机变量, 记S_n=X_1+\cdots+X_n, M_n=\max\limits_k\le n|S_k|, n\ge 1. 本文在充分必要条件下给出了M_n和S_n的对数律之精确渐近性.

Abstract: Let X_1,X_2,\cdots be i.i.d. random variables, and set S_n=X_1+\cdots+X_n, M_n=\max\limits_k\le n|S_k|, n\ge 1. The precise rates in the law of the logarithm for M_n are obtained under sufficient and necessary conditions.