Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements  

作　　者：Andrew ROSALSKY Le Van THANH Nguyen Thi THUY 

机构地区：[1]Department of Statistics,University of Florida,Gainesville,FL 32611-8545,USA [2]Department of Mathematics,Vinh University,Vinh,Nghe An,Viet Nam [3]High School for Gifted Students,Vinh University,Vinh,Nghe An,Viet Nam

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1727-1740,共14页数学学报（英文版）

摘　　要：In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.

关 键 词：Double sum mean convergence Rademacher type p Banach space Banach space valued random element M-dependent random elements 

分 类 号：O177.2[理学—数学]