NA列部分和乘积的极限定理

Limit theorem for the product of the partial sums of NA random variables

讨论NA列部分和乘积的中心极限定理和几乎处处中心极限定理,并将独立同分布(i.i.d.)随机变量序列的部分和乘积的几乎处处中心极限定理的权重由dn=exp(logαn)/n推广到dn=log(cn+1)/cnexp(logαn),0≤α<1 2的情形,其中0<cn→∞,limn→∞(cn+1)/cn=c<∞.

The central limit theorem and almost sure central limit theorem for products of some partial sums of a sequence of NA random variables were discussed. We furtherly extended weight sequence dn=exp（logαn）/n to dn=log（cn＋1）/cnexp（logαn） for the almost sure central limit theorem of independent identically distributed （i.i.d.） random variables, where 0〈Cn→∞,lim n-∞Cn/Cn＋1=c〈∞.