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Research Article | Open Access

Complete convergence and complete integral convergence for weighted sums of widely acceptable random variables under the sub-linear expectations

Chengcheng Jia, Qunying Wu( )
College of Science, Guilin University of Technology, Guilin 541006, China
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Abstract

Since the concept of sub-linear expectation space was put forward, it has well supplemented the deficiency of the theoretical part of probability space. In this paper, we establish the complete convergence and complete integration convergence for weighted sums of widely acceptable (abbreviated as WA) random variables under the sub-linear expectations with the different conditions. We extend the complete moment convergence in probability space to sublinear expectation space.

Keywords

sub-linear expectationcomplete convergencecomplete integral convergenceWA random variables
CLC number: 60F15

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8430-8448
DOI: 10.3934/math.2022470

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Cite this article:
Jia C, Wu Q. Complete convergence and complete integral convergence for weighted sums of widely acceptable random variables under the sub-linear expectations. AIMS Mathematics, 2022, 7(5): 8430-8448. https://doi.org/10.3934/math.2022470

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Received: 28 November 2021
Revised: 12 February 2022
Accepted: 14 February 2022
Published: 15 May 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)