截断和乘积几乎处处中心极限定理的注记

Note on the Almost Sure Central Limit Theorem for Product of Trimmed Sums

设{X_n,n≥1}为连续独立同中尾分布的正平方可积随机变量序列.对于固定的常数a>0,T_n(a)=S_n-S_n(a)为截断和.利用截断和的极限性质及大数定律,在一般的权重条件下,证明了截断和乘积的几乎处处中心极限定理.

Let{Xn,n≥1}be a sequence of i.i.d.positive square integrable random variables with continuous and independent medium tail distribution function. For a fixed constant a 〉0,T_n（a）=S_n-S_n（a）denoted the trimmed sum,we proved the almost sure central limit theorem for the product of trimmed sums under the general weight by using the limit properties of the trimmed sums and the law of large numbers.