摘要
设随机变量Ｘ１，Ｘ２，…ｉｉｄ；称Ｕｎ＝１≤ｉ＜ｊ≤ｎＸｉＸｊ，为两两乘积之和，本文意在给出 Ｕｎ／ｎ~２→０即文中（０．３）式成立的充分必要条件．我们在这部分工作中虽未能彻底解决这个问题，但却揭示出这类条件与Ｓｎ／ｎ→０（Ｓｎ＝ｎｉ＝１Ｘｉ）之条件间的本质上的不同之处，就是说，这是一类不能完全用Ｘ１的矩来刻划的条件，它们要更为深层次地依赖于Ｘ１的尾分布性质．
Let X1, X2,... be independent identically distributed (iid) random variables, Un = 1≤i＜j≤nXiXj is said to be pairwise products sum. In this paper, we give necessary and sufficient conditions for Un/n^2 → 0 (i.e. (0.3)). Though this question in this part has not been settled thoroughly yet, it reveals an essential distinction between this class conditions and these ones of Sn/n → 0 (Sn = n=1 Xi), i.e. this class conditions can not been characterized thoroughly by the moment of X1, it need to depend deeply on the tail probabality property of X1.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第5期875-886,共12页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金!(19671078)
中国科学院特别支持经费
江苏省教委自然科学基金
