独立随机变量序列重对数律的一个注记

A Note About the Law of the Iteravated Logarithm for independent Random

摘要: ｛X_i｝为独立随机变量序列，Ｅ（X_i）＜＋∞，Ｅ(X_i²)＜＋∞（i＝１，２，…），当中心极限定理中的余项△_n＝O((lnBn lnlnBn…(ln_kBn)^1＋δ)^-1)时，本文得出结论:\overline\lim \fracS_n\sqrt2 B_n \ln \ln B_n=1 \quad a.s..

Abstract: Let X_i be a sequences of independent random variable with E（X_i） = 0, E（X_i²）＜ ∞ （i = 1, 2,… ）, where the remainder of the central limit theorem is: △_n＝O((lnBn lnlnBn…(ln_kBn)^1＋δ)^-1), we prove the result as follow:\overline\lim \fracS_n\sqrt2 B_n \ln \ln B_n=1 \quad a.s..