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Research Article | Open Access

The convergence rate for the laws of logarithms under sub-linear expectations

College of Science, Guilin University of Technology, Guilin 541004, China
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Abstract

Let { X n ; n ≥ 1 } be a sequence of independent and identically distributed random variables in a sub-linear expectation space ( Ω , H , E ^ ). The necessary and sufficient conditions for the convergence rate on the laws of the logarithms and the law of the iterated logarithm are obtained.

Keywords

sub-linear expectationconvergence ratelaws of logarithmslaw of the iterated logarithm
CLC number: 60F15

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 24786-24801
DOI: 10.3934/math.20231264

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Cite this article:
Wu Q. The convergence rate for the laws of logarithms under sub-linear expectations. AIMS Mathematics, 2023, 8(10): 24786-24801. https://doi.org/10.3934/math.20231264

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Received: 20 May 2023
Revised: 27 July 2023
Accepted: 10 August 2023
Published: 15 October 2023
©2023 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)