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Research Article | Open Access

Law of the single logarithm for randomly weighted sums of dependent sequences and an application

Yi Wu, Duoduo Zhao( )
School of Big Data and Artificial Intelligence, Center of Applied Mathematics, Chizhou University, Chizhou, 247000, China
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Abstract

In this work, the law of the single logarithm for randomly weighted sums of widely orthant dependent random variables was studied, which improved and generalized some corresponding results in the literature. As an application, the rate of complete convergence for random weighting estimation with widely orthant dependent samples was obtained under general assumptions. Some numerical analyses were also conducted to confirm the theoretical results.

Keywords

law of the single logarithmrandomly weighted sumscomplete convergencerandom weighting estimationwidely orthant dependent
CLC number: 60F15, 62G05

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 10141-10156
DOI: 10.3934/math.2024496

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Wu Y, Zhao D. Law of the single logarithm for randomly weighted sums of dependent sequences and an application. AIMS Mathematics, 2024, 9(4): 10141-10156. https://doi.org/10.3934/math.2024496

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Received: 22 December 2023
Revised: 04 March 2024
Accepted: 06 March 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)