Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

作     者：Yi WU Xue Jun WANG Yi WU;Xue Jun WANG

作者机构：School of Big Data and Artificial IntelligenceChizhou UniversityChizhou 247000P.R.China School of Big Data and StatisticsAnhui UniversityHefei 230601P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第4期

页      面：1127-1142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：Supported by the Outstanding Youth Research Project of Anhui Colleges(Grant No.2022AH030156) 

主　　题：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 

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 *** 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(1p2)***,the complete convergence and strong law of large numbers are established under some mild *** application to multivariate simple linear regression model is also provided.