B值随机变量序列一类加权和的完全收敛性  

Complete Convergence for Some Weighted Sums of B-Valued Random Variables

作　　者：陈传勇[1] 陈平炎[2] 

机构地区：[1]仲恺农业工程学院计算科学学院,广州510225 [2]暨南大学数学系,广州510630

出　　处：《应用数学学报》2015年第3期526-534,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271161)资助项目

摘　　要：在没有任何几何假设条件下,本文获得了取值于Banach空间随机变量序列一类加权和的完全收敛性,推广和改进了已有的结果.作为应用获得了取值于p型Banach空间随机变量序列的完全收敛性,特别获得了经验过程在L_p范数下的完全收敛性,1≤p<2.Without any geometrical assumption on the underlying Banach space, the com- plete convergence for some weighted sums of B-valued random variables are obtained. The main results extend and generalize the well-known results. As the applications, the similar results are abtained for the weighted sums of the random variables taking valued in p- type Banach sapce, and in particular for the empirical processes under the Lp norm, where 1≤p〈2.

关 键 词：B值随机变量序列 完全收敛性 依概率收敛 Banach空间的型 经验过程 

分 类 号：O211.4[理学—概率论与数理统计]