随机变量阵列加权和的r阶矩完全收敛性  

Complete rth Moment Convergence forWeighted Sums of Random Variable Arrays

作　　者：王柳柳 胡学平 WANG Liuliu;HU Xueping(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2023年第1期26-31,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家社科基金面上项目(21BTJ040);安庆师范大学院级研究生学术创新项目(2021yjsXSCX040)。

摘　　要：独立同分布变量序列和相依变量序列的收敛性质研究一直是概率极限理论的研究热点。本文研究了随机变量阵列加权和的r阶矩完全收敛性。利用Marcinkiewicz-Zygmund不等式或Rosenthal型不等式和截尾法,获得了随机变量阵列加权和的r阶矩完全收敛的一般条件。同时,结合这些一般条件推广和改进了独立同分布或相依随机变量序列矩完全收敛性的相关成果。The study of the convergence properties of sequences of independent identically distributed variables arrays and dependent sequences has been a hot topic of research in probability limit theory.In this article,the complete rth moment convergence of weighted sums of random variable arrays is investigated.By utilizing Marcinkiewicz-Zygmund inequality,Rosenthal type inequality and the truncated method,the general conditions for complete rth moment convergence of the weighted sums of random variable arrays are obtained.In combination with these general conditions,we extend and improve the related results on the complete moments convergence for arrays of independent identically distributed or dependent random variables.

关 键 词：Marcinkiewicz-Zygmund不等式 Rosenthal型不等式 加权和 矩完全收敛性 

分 类 号：O211.4[理学—概率论与数理统计]