Precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectations

Lizhen Huang; Qunying Wu; Lizhen Huang; Qunying Wu

doi:10.3934/math.2023449

AIMS Mathematics

2023, Volume 8, Issue 4: 8964-8984. doi: 10.3934/math.2023449

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Research article

Precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectations

Lizhen Huang ^1,2,
Qunying Wu ^{1,2
,
,}

1.
College of Science, Guilin University of Technology, Guilin 541004, China
2.
Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin 541004, China

Received: 11 October 2022 Revised: 31 January 2023 Accepted: 01 February 2023 Published: 09 February 2023
MSC : 60F15

The aim of this paper is to study and establish precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectation space. The methods and tools in this paper are different from those used to study precise asymptotics theorems in probability space. We extend precise asymptotics for complete integral convergence from the classical probability space to sub-linear expectation space. Our results generalize corresponding results obtained by Fu and Yang^[13]. We further extend the limit theorems in classical probability space.
- precise asymptotics,
- complete integral convergence,
- the law of the logarithm,
- sub-linear expectations
Citation: Lizhen Huang, Qunying Wu. Precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectations[J]. AIMS Mathematics, 2023, 8(4): 8964-8984. doi: 10.3934/math.2023449

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Abstract

The aim of this paper is to study and establish precise asymptotics for complete integral convergence in the law of the logarithm under the sub-linear expectation space. The methods and tools in this paper are different from those used to study precise asymptotics theorems in probability space. We extend precise asymptotics for complete integral convergence from the classical probability space to sub-linear expectation space. Our results generalize corresponding results obtained by Fu and Yang^[13]. We further extend the limit theorems in classical probability space.

References

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