| In this paper,we make a study on the complete convergence of moving average processes of generalized pairwise Negatively Quadrant Dependent (NQD) random variables.It is well known,that the convergence theorem is one of the most important results in probability theory. It is longtime before people study the convergence theorem and limit theorem. In the early time,people studied the convergence theorem on i.i.d.real random variables. Recently,many people have studied the properties of pairwise Negatively Quadrant Dependent(NQD) sequences,and they have obtained many similiar results with independent random variables. Furthermore,some scholars try to study the qualities of complete convergence of moving average processes on the base of the convergence of random variables,and they have obtained many important results.In the 50's and in the 60's,after the limit theory about the sum of i.i.d.random variables get the perfect developement, on the one hand because of the need of statistical problem, for example the sample is not independent, on the other hand because of the need of theory study and the other branch, Dependent random variables have a lot of important application. So, it is important to study pairwise Negatively Quandrant Dependent sequences. In this paper, I try to use some results given by the formar scholars and study the complete convergence of moving average processes of dependent random variables.This paper has two parts. In the first section, we introduce the con-cepts of NQD and some lemmas. In the second section, we give and prove the complete convergence of moving average processes of generalized NQD sequence.In this paper, we introduce the following definitions.lemmas and result.Definition 1 Two random variables X and Y are said to be NQD (Negative Quadrant Dependent), ifP(X 1} are said to be LNQD(Linear Negative Quadrant Dependent), if for any disjoint finite subsets A,BcNd and any positive real numbers r^r,, ￡ uXi and ￡ TjXj are NQD .Definition 3 Random variables Xi,X2,---,Xk axe said to be Negatively Associated(NA), if for every pair of disjoint subsets Ai, A2 of {1,2, ? ? ?, n}Cov{h{xi,ie Al),f2{xjJ € A2)) < 0whenever f\ and f2 are increasing "NA" may also refer to the vector X = (Xi, X2, ■? ?, XK) or to the underlying distribution of X. Additionally, "NA" may denote Negative Association.ooLemma 1([8] Lemma 2.1) Let X) ^t be an absolutely convergentt=—oo oo ooseries of real numbers with a = J2 Q-i,b = ￡ |oj|. Let $ : [—b,b] —> R bet=—OO t=—00a function with the following properties:(1) $ is bounded, $ is continuous at a.(2) 38 > 0 and BC > 0, such that |$(x)| < C\x\ , for all \x\ < S , then1 oo i+nlim — > $( > o,-) = $(a).addition: Let $(x) = |x|p,p > 1, then-I oo i+nLemma 2 ^ Let /i(a;) > 0 be a slowly varying function as x —> oo , then(1) lim T^f = 1, V* > 0;lim ^^ = 1, Vw > 0.(2) lim sup M = 1.(3) lim x*./i(a;) = oo, lim x~6h(x) =0, VJ > 0.Theorem 1 Let {Yi'} — oo < i < oo} be a r.v. sequence of identical distribute, and satisfying(A). ap> 1,1 < p <2, a < 1 , EY\ = 0. {a*;—oo i+kYi, k > 1. and let l(x) > 0 be a slowly varying function as x —> oo ,t=—oo 0,()p{| ￡ *| > ena} < oo.n=l fc=l...
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