B值随机变量阵列加权和的完全收敛性

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

中文关键词:  完全收敛  行间独立的B值r.v.阵列  正则变化函数  加权和

英文关键词:array of rowwise independent B-valued random variables  complete convergence  regular varying function  weighted sum.

中文摘要:

      设{X_ni:1≤i≤n,n≥1}为行间独立的B值r.v.阵列,g(z)是指数为1/p的正则变化函数,r>0,{ani 1≤t≤n,n≥1}为实数阵列,本文得到了使(?)成立的条件,推广并改进了Stout及Sung等的著名结论.

英文摘要:

      Let {X_ni:1≤i≤n,n≥1} be an array of rowwise independent B-valued random variables, and let g(x) be a regular varying function with index 1/P(P>0) . Let {a_ni:1≤i≤n,n≥1} be an array of real numbers. Let r>0 . The sufficient conditions such that (?) are obtained. The wellknown results by Stout and Sung etc. are extended.