On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence-Reference-Cited by-同舟云学术

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

Published:2024-02-01 Issue:1 Volume:74 Page:209-220
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Dzung Nguyen Chi¹,Hien Nguyen Thi Thanh²

Affiliation:

1. Vietnam Academy of Science and Technology 18 Hoang Quoc Viet Hanoi Vietnam

2. School of Applied Mathematics and Informatics Hanoi University of Science and Technology 1 Dai Co Viet Hanoi Vietnam

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/ms-2024-0016/pdf

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