行为NA的随机变量阵列加权和的完全收敛性

Complete Convergence of Weighted Sums for Arrays of Rowwise NA Random Variables

{Xni,1≤i≤n,n∈N}是行为NA的随机变量阵列,且一致有界于随机变量X,p>0,E｜X｜2p<a2ni=o(1∞,EXni=0(1≤i≤n,n∈N),{ani,1≤i≤n,n∈N}是实数阵列,max｜ani｜=O(1logn),n1/p),∑n1≤i≤ni=1C0,推广了Stout及Taylor等相应的结果.

Let {X(ni),1≤i≤n,n∈N} be an arrays of rowwise NA random variables,such that EX(ni)=0,1≤i≤n,n∈N,and uniformly bounded by a random variable X,E|X|^(2p)<∞,p>0,Let{a(ni),1≤i≤n,n∈N} be an arrays of real numbers such that (max)1≤i≤n|a(ni)|=O(1n^(1/p)) and '∑ni=1a^2(ni)=o'(1logn),then '∑ni=1a(ni)X(ni)'→0 completely,which extend the theorem of Stout and Taylor.