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

被引：0

作者：

Andrew ROSALSKY ^{[1
]}

L Vn THNH ^{[2
]}

Nguyen Thi THUY ^{[3
]}

机构：

[1] Department of Statistics, University of Florida

[2] Department of Mathematics, Vinh University

[3] High School for Gifted Students, Vinh

来源：

Acta Mathematica Sinica,English Series | 2024年 / 07期

关键词：

D O I：

暂无

中图分类号：

O177.2 [巴拿赫空间及其线性算子理论];

学科分类号：

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.

引用

页码：1727 / 1740

页数：14

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