An Almost Sure Central Limit Theorem for Self-normalized Weighted Sums  

作　　者：Yong ZHANG Xiao-yun YANG 

机构地区：[1]College of Mathematics, Jilin University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第1期79-92,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10971081, 11101180).

摘　　要：Let X, X1, X2, be a sequence of nondegenerate i.i.d, random variables with zero means, which is in the domain of attraction of the normal law. Let （ani, 1 ≤ i ≤n,n ≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums.Let X, X1, X2, be a sequence of nondegenerate i.i.d, random variables with zero means, which is in the domain of attraction of the normal law. Let （ani, 1 ≤ i ≤n,n ≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums.

关 键 词：almost sure central limit theorem self-normalized weighted sums domain of attractio of thenormal law 

分 类 号：O211.4[理学—概率论与数理统计] O211.5[理学—数学]