Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011, Article ID 279754, 13 pages doi: Research Article On Strong Law of Large Numbers for Dependent Random Variables Zhongzhi Wang Faculty of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, China Correspondence should be addressed to Zhongzhi Wang, wzz30@ Received 16 December 2010; Accepted 3 March 2011 Academic Editor: Vijay Gupta Copyright q 2011 Zhongzhi Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We discuss strong law of large. | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 279754 13 pages doi 2011 279754 Research Article On Strong Law of Large Numbers for Dependent Random Variables Zhongzhi Wang Faculty of Mathematics and Physics Anhui University of Technology Ma anshan 243002 China Correspondence should be addressed to Zhongzhi Wang wzz30@ Received 16 December 2010 Accepted 3 March 2011 Academic Editor Vijay Gupta Copyright 2011 Zhongzhi Wang. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We discuss strong law of large numbers and complete convergence for sums of uniformly bounded negatively associate NA random variables RVs . We extend and generalize some recent results. As corollaries we investigate limit behavior of some other dependent random sequence. 1. Introduction Throughout this paper let N denote the set of nonnegative integer let X Xn n e N be a sequence of random variables defined on probability space Q F P and put Sn 2ik i Xk. The symbol C will denote a generic constant 0 C to which is not necessarily the same one in each appearance. In 1 Jajte studied alarge class of summability method as follows asequence Xn n 1 is summable to X by the method h g if 1 n Xk X 7X as n 7 to g n ki1 hk The main result of Jajte is as follows. Theorem . Let g be a positive increasing function and h - a positive function such that fiiyi g y h y satisfies the following conditions. 1 For some d 0 ộ fi is strictly increasing on d to with range 0 to . 2 There exist C and a positive integer k0 such that fi y 1 y C y k0. 3 There exist constants a and b such that ộ2 s ỊSTO .1 ộ2 xỴ dx as b s d. 2 Journal of Inequalities and Applications Then for . random variables Xn n e N 1 1 Xk ệ k g n z h k . iff E 1 X j TO where Ộ 1 is the inverse of function Ộ
