负相关随机变量阵列加权和的矩完全收敛性.pdf

??????????????2013?2?Chinese Journal of Applied Probabilityand Statistics Feb. plete Moment Convergence of Weighted Sums forArrays of Rowwise Negatively Associated RandomVariables?Guo Mingle Zhu Dongjin Ren Yong(School of Mathematics puter Science, Anhui Normal University, Wuhu, 241003)plete moment convergence of weighted sums for arrays of rowwise negatively associ-ated random variables is investigated. The results of Baek et al. (2008) plemented. As anapplication, plete moment convergence of moving average processes based on a negativelyassociated random sequences is obtained, which improves the result of Li et al. (2004).Keywords:Sequence of negatively associated random variables, weighted sums, completemoment convergence, complete convergence, moving average Subject Classi?cation:60F15.§1. IntroductionLet{Xn, n≥1}be a sequence of random variables and, as usual, setSn=nPi=1Xi, n≥{Xn, n≥1}are independent and identically distributed (.), Baum and Katz(1965) proved the following remarkable result concerning the convergence rate of the tailprobabilitiesP{|Sn|> 2n1/p}for any2 > A[1]Let 0< p <2 andr≥p. Then∞Pn=1nr/p?2P{|Sn|> 2n1/p}<∞for all2 >0,if and only ifE|X1|r<∞, whereEX1= 0 whenever 1≤p < is an interesting and substantial literature of investigation apropos of extendingthe Baum-Katz Theorems along a variety of di?erent paths. One of these extensions isdue to Chow (1988) who established the following re?nement which is plete momentconvergence result for sums of . random variables.?Supported by the National Natural Science Foundation of China (11201004 and 11271020), the Key Project ofChinese Ministry of Education (211077) and the Anhui Provincial Natural Science Foundation (10040606Q30 and1208085MA11).Received May 23, 2011. Revised August 20, 2011.??? ????????:?????э?????????????43Theorem B[2]LetEX1= 0, 1≤p <2 andr≥p. Suppose thatE[|X1|r+|X1|·log(1 +|X1|)]<∞. Then∞Pn=1nr/p?2?1/pE(|Sn| ?2n1/p)+<∞for