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Research Article | Open Access

Almost sure convergence theorems for arrays under sub-linear expectations

Li Wang, Qunying Wu( )
College of Science, Guilin University of Technology, Guilin 541006, China
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Abstract

In this work, inspired by the extended negatively dependent arrays, we want to obtain a limit theorem on almost sure convergence relying on non-additive probabilities. Meanwhile, we offer two appropriate upper integration conditions as an application, allowing us to derive deterministic bounds based on logarithm. Furthermore, these results extend the limit theorems in classical probability space.

Keywords

sub-linear expectationalmost sure convergenceextended negative dependencelaw of the logarithmweakly mean dominated
CLC number: 60F15

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AIMS Mathematics
Volume 7 Issue 10,
October 2022
Pages 17767-17784
DOI: 10.3934/math.2022978

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Wang L, Wu Q. Almost sure convergence theorems for arrays under sub-linear expectations. AIMS Mathematics, 2022, 7(10): 17767-17784. https://doi.org/10.3934/math.2022978

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Received: 12 May 2022
Revised: 20 July 2022
Accepted: 27 July 2022
Published: 15 October 2022
©2022 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)