巴拿赫空间有值随机元素规范化双和最大值的一些均值收敛定理

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2024-04-20 DOI:10.1007/s10114-024-2669-1

Andrew Rosalsky, Lê Vǎn Thành, Nguyen Thi Thuy

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引用次数: 0

摘要

在这一对应关系中，我们建立了巴拿赫空间值随机元素的规范化双和最大值的均值收敛定理。大部分结果都与依赖 M 的随机元素有关。我们扩展并改进了巴拿赫空间中随机元素均值收敛文献中的一些特殊情况。本文的主要贡献之一是简化和改进了 Li、Presnell 和 Rosalsky 最近的一个结果 [《数学不等式学报》，16，117-126 (2022)]。本文还证明了一个新的最大不等式，该不等式适用于依赖 M 的随机元素的双和，这可能会引起人们的兴趣。四个例子说明了结果的尖锐性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.