Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : A note on the complete convergence for sequences of pairwise NQD random variables | Huang et al. Journal of Inequalities and Applications 2011 2011 92 http content 2011 1 92 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access A note on the complete convergence for sequences of pairwise NQD random variables Haiwu Huang1 2 Dingcheng Wang 1 Qunying Wu2 and Qingxia Zhang1 Correspondence huanghaiwu@ 1School of Mathematics Science University of Electronic Science and Technology of China Chengdu 610054 PR China Full list of author information is available at the end of the article Springer Abstract In this paper complete convergence and strong law of large numbers for sequences of pairwise negatively quadrant dependent NQD random variables with non-identically distributed are investigated. The results obtained generalize and extend the relevant result of Wu Acta. Math. Sinica. 45 3 617-624 2002 for sequences of pairwise NQD random variables with identically distributed. 2000 MSC 60F15. Keywords pairwise NQD random variable sequences complete convergence almost sure convergence 1 Introduction In many stochastic models the assumption of independence among random variables is not plausible. So it is necessary to extend the concept of independence to dependence cases one of these dependence structures is negatively quadrant dependent NQD random variables. The concept of NQD random variables was introduced by Lehmann 1 . Definition 1 Two random variables X and Y are said to be NQD random variables if for any x y e R P X x Y y P X x P Y y . A sequence of random variables Xn n 1 is said to be pairwise NQD random variables if for all i j i j e N Xi and Xj are NQD random variables. Obviously a sequence of pairwise NQD random variables is a family of very wide scope which contains sequences of pairwise independent random variables. Many known types of negative dependence such as negatively orthant dependent NOD random variables and negatively associated NA 2 random .
