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

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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.
作者 Andrew ROSALSKY Le Van THANH Nguyen Thi THUY
机构地区 Department of Statistics Department of Mathematics High School for Gifted Students
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第7期1727-1740,共14页 数学学报（英文版）
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—基础数学]
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Acta Mathematica Sinica,English Series
2024年 第7期

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