论希尔伯特空间中成对独立随机向量的 von Bahr-Esseen 不等式及其在均值收敛中的应用

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0016

Nguyen Chi Dzung, Nguyen Thi Thanh Hien

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引用次数: 0

摘要

在这篇论文中，我们证明了希尔伯特空间中成对独立随机向量的 von Bahr-Esseen 矩不等式。我们在 von Bahr-Esseen 矩不等式中的常数优于 Chen 等人在实值随机变量中得到的常数[The von Bahr-Esseen moment inequality for pairwise independent random variables and applications, J. Math. Analys.Anal.419 (2014), 1290-1302] 以及 Chen 和 Sung [Generalized Marcinkiewicz-Zygmund type inequalities for random variables and applications, J. Math. Inequal.Inequal.10(3) (2016), 837-848].然后应用该结果获得希尔伯特空间中行独立和成对独立随机向量三角阵列的均值收敛定理。文献中的一些结果得到了扩展。

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On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence

In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [The von Bahr–Esseen moment inequality for pairwise independent random variables and applications, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.