Exponential inequalities and a strong law of large numbers for END random variables under sub-linear expectations

Haiye Liang; Feng Sun; Haiye Liang; Feng Sun

doi:10.3934/math.2023795

AIMS Mathematics

2023, Volume 8, Issue 7: 15585-15599. doi: 10.3934/math.2023795

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Exponential inequalities and a strong law of large numbers for END random variables under sub-linear expectations

Haiye Liang ¹,
Feng Sun ^{2
,
,}

1.
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
2.
College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China

Received: 10 March 2023 Revised: 17 April 2023 Accepted: 23 April 2023 Published: 27 April 2023
MSC : 60F15

The focus of our work is to investigate exponential inequalities for extended negatively dependent (END) random variables in sub-linear expectations. Through these exponential inequalities, we were able to establish the strong law of large numbers with convergence rate $ O\left(n^{-1/2}\ln^{1/2}n\right) $. Our findings in sub-linear expectation spaces have extended the corresponding results previously established in probability space.
- sub-linear expectation,
- exponential inequality,
- strong law of large numbers,
- convergence rate,
- END random variables
Citation: Haiye Liang, Feng Sun. Exponential inequalities and a strong law of large numbers for END random variables under sub-linear expectations[J]. AIMS Mathematics, 2023, 8(7): 15585-15599. doi: 10.3934/math.2023795

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Abstract

The focus of our work is to investigate exponential inequalities for extended negatively dependent (END) random variables in sub-linear expectations. Through these exponential inequalities, we were able to establish the strong law of large numbers with convergence rate $ O\left(n^{-1/2}\ln^{1/2}n\right) $. Our findings in sub-linear expectation spaces have extended the corresponding results previously established in probability space.

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