Exponential inequalities for associated random variables and strong laws of large numbers

作     者：Shan-chao YANG & Min CHEN Deptartment of Mathematics, Guangxi Normal University, Guilin 541004, China Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 

作者机构：Deptartment of Mathematics Guangxi Normal University Guilin 541004 China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第5期

页      面：705-714页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：the National Natural Science Fbundation of China (Grant Nos. 10161004, 70221001, 70331001) the Natural Science Foundation of Guangxi Province of China (Grant No. 04047033) 

主　　题：associated random variable exponential inequality strong law of large numbers rate of convergence 60E15 60F15 

摘      要：Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.