随机序列几乎处处中心极限定理的注记

A Note on Almost Sure Central Limit Theorems for Random Sequences

设{S_k,k≥1}为一随机序列,满足几乎处处中心极限定理;{T_k,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{S_k+T_k,k≥1}和{S_k/T_k,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{S_k,k≥1}be a random sequence satisfying the almost sure central limit theorem,and{T_k,k≥1}be a random sequence with T_k→0(or 1)a.s.By using the limit theory,we proved that{S_k+T_k,k≥1}and{S_k/T_k,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.