随机序列几乎处处中心极限定理的注记

摘要

设{Sk,k≥1}为一随机序列,满足几乎处处中心极限定理;{Tk,k≥1}为一随机序列,几乎处处收敛到0或1.利用极限理论证明{Sk+Tk,k≥1}和{Sk/Tk,k≥1}也满足几乎处处中心极限定理,并给出其线性过程、自正则和、线性模型中误差方差估计、部分和乘积等实例.%Let {Sk,k≥1}be a random sequence satisfying the almost sure central limit theorem,and{Tk,k≥1}be a random sequence with Tk→0(or 1)a.s.By using the limit theory,we proved that{Sk+Tk,k≥1}and {Sk/Tk,k≥1}satisfied the almost sure central limit theorem,and gave some examples such as linear processes,self-normalized sums,error variance estimates in linear models and products of partial sums.