Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors  

作　　者：Yi WU Xue Jun WANG 

机构地区：[1]School of Big Data and Artificial Intelligence,Chizhou University,Chizhou 247000,P.R.China [2]School of Big Data and Statistics,Anhui University,Hefei 230601,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1127-1142,共16页数学学报（英文版）

基　　金：Supported by the Outstanding Youth Research Project of Anhui Colleges(Grant No.2022AH030156)。

摘　　要：Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.

关 键 词：Martingale difference random vectors weighted sums Marcinkiewicz–Zygmund type weak law of large numbers complete convergence strong law of large numbers multivariate simple linear regression model 

分 类 号：O211.4[理学—概率论与数理统计]