剩余h-可积条件下相依随机变量加权和的收敛性质(英文)  

Convergence for Weighted Sums of Dependent Random Variables under Residual h-Integrability Assumption

作　　者：胡学平[1,2] 方国华[2] 

机构地区：[1]安庆师范学院数学与计算科学学院,安庆246133 [2]河海大学水利水电学院,南京210098

出　　处：《应用概率统计》2013年第1期64-74,共11页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the Natural Science Foundation of Anhui Province(KJ2013A126,KJ2012Z233)

摘　　要：设{Xni,un≤i≤vn,n≥1}与{ani,un≤i≤vn,n≥1}分别为一个随机阵列和一个常数阵列.本文首先引入了随机阵列{Xni,un≤i≤vn,n≥1}关于常数阵列{ani,un≤i≤vn,n≥1}剩余h-可积的概念,它是弱于h-可积,Cesaroα-可积等其它相关可积的定义.然后在这一可积的定义和适当的条件下,我们研究了相依随机序列加权和的强收敛性和平均收敛性,推广并改进了相关文献已有结果.Let {Xni,un≤i≤vn,n≥1} be an array of random variables and {ani,un≤i≤vn,n≥1} be an array of constants.A new concept of integrability（call residually h-integrability） for an array of random variables {Xni} with respect to an array of constants {ani} is introduced,which is weaker than other related notions of integrability,such as h-integrability,Cesaro α-integrability.Under this assumption of integrability and appropriate conditions on the array of weights,we investigate strong convergence and mean convergence for weighted sums of dependent random variables.Some related results in literature are extended and improved.

关 键 词：Φ-混合序列 两两LCND序列 r-阶平均收敛 一致可积 加权和 

分 类 号：O211.4[理学—概率论与数理统计]