END随机变量的完全矩收敛和完全积分收敛

Complete moment convergence and complete integral convergence for END random variables

设{X,X_n,n≥1}是同分布的END(extended negatively dependent)随机变量序列,Sn=n∑i=1,n≥1。研究了完全矩收敛性∞∑n=1n^r-2-1/pqanE(max1≤k≤n∣Sk∣1/q-εbn1/pq)^+<∞,?ε>0在r>1,q>0,0<p<2,an=1,bn=n和p=2,an=(logn)^-1/2q,bn=nlogn的情况下,与完全积分收敛的一些等价结论。所得结果推广了NA(negatively associated)变量和NOD(negatively orthant dependent)变量的若干相应结果。

Let{X,X_n,n≥1}be a sequence of extended negatively dependent(END)random variables with identical distribution,and Sn=n∑i=1,n≥1.The equivalent conditions between complete moment convergence∞∑n=1n^r-2-1/pqanE(max1≤k≤n∣Sk∣1/q-εbn1/pq)^+<∞,?ε>0 and complete integral convergence were investigated under two cases:r>1,q>0,0<p<2,a_n=1,b_n=n and p=2,an=(logn)^-1/2q,bn=nlogn.The results obtained generalize the corresponding ones for negatively associated(NA)random variables and negatively orthant dependent(NOD)random variables.