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

Qunying Wu; Qunying Wu

doi:10.3934/math.20231264

AIMS Mathematics

2023, Volume 8, Issue 10: 24786-24801. doi: 10.3934/math.20231264

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Research article

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

Qunying Wu ^,

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

Received: 20 May 2023 Revised: 27 July 2023 Accepted: 10 August 2023 Published: 23 August 2023
MSC : 60F15

Let $ \{X_n; n\geq1\} $ be a sequence of independent and identically distributed random variables in a sub-linear expectation space $ (\Omega, \mathcal{H}, \hat{\mathbb{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.
- sub-linear expectation,
- convergence rate,
- laws of logarithms,
- law of the iterated logarithm
Citation: Qunying Wu. The convergence rate for the laws of logarithms under sub-linear expectations[J]. AIMS Mathematics, 2023, 8(10): 24786-24801. doi: 10.3934/math.20231264

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Abstract

Let $ \{X_n; n\geq1\} $ be a sequence of independent and identically distributed random variables in a sub-linear expectation space $ (\Omega, \mathcal{H}, \hat{\mathbb{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.

References

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