两两NQD阵列加权和的L^r收敛性

L^r Convergence for the Weighted Sums of Pairwise NQD Random Arrays

两两NQD列是一类非常广泛的随机变量列,后来的许多负关联列都是在此基础上繁衍出来的.该文讨论了零均值的行两两NQD阵列{Xni;1≤i≤kn↑∞,n∈N}在满足r(1≤r<2)阶h-可积条件下的Lr收敛性,即:limn→∞E|kn-1/rSnkn|r=0,获得了与独立情形一致的结果,全面改进了陈平炎关于两两NQD随机序列Lr收敛性的工作.

Pairwise NQD sequence is a class of random variable sequence, which is very widespread, many of the negative dependence sequences are derived from it later. In this paper, the author discusses the L^r convergence for the weighted sums of pairwise NQD random arrays under r-th h-integrability, that is： limEn→∞｜kn^-1/rSnkn｜^r=0, it is the same as that in the independent case. Thus, the results in the previous paper [5] are extended and fully improved.