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

Chengcheng Jia; Qunying Wu; Chengcheng Jia; Qunying Wu

doi:10.3934/math.2022470

AIMS Mathematics

2022, Volume 7, Issue 5: 8430-8448. doi: 10.3934/math.2022470

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Research article

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

Received: 28 November 2021 Revised: 12 February 2022 Accepted: 14 February 2022 Published: 28 February 2022
MSC : 60F15

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.
- sub-linear expectation,
- complete convergence,
- complete integral convergence,
- WA random variables
Citation: Chengcheng Jia, Qunying Wu. Complete convergence and complete integral convergence for weighted sums of widely acceptable random variables under the sub-linear expectations[J]. AIMS Mathematics, 2022, 7(5): 8430-8448. doi: 10.3934/math.2022470

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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.

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