The convergence of the sums of independent random variables under the sub-linear expectations

DOI10.1007/S10114-020-8508-0zbMath1434.60102arXiv1902.10872OpenAlexW2917004389MaRDI QIDQ1987563

Yanyan Li

Publication date: 15 April 2020

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.10872

zbMATH Keywords

independencecapacitycentral limit theoremsub-linear expectationLévy maximal inequality

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (6)

Heyde's theorem under the sub-linear expectations ⋮ On the laws of the iterated logarithm under sub-linear expectations ⋮ Note on precise rates in the law of iterated logarithm for the moment convergence of i.i.d.: random variables under sublinear expectations ⋮ Capacity inequalities and strong laws for \(m\)-widely acceptable random variables under sub-linear expectations ⋮ Complete convergence theorems for arrays of row-wise extended negatively dependent random variables under sub-linear expectations ⋮ The sufficient and necessary conditions of the strong law of large numbers under sub-linear expectations

Cites Work

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• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• Strong laws of large numbers for sub-linear expectations
• Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm
• A general central limit theorem under sublinear expectations
• Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations
• Strong laws of large numbers for sublinear expectation under controlled 1st moment condition
• Marcinkiewicz's strong law of large numbers for nonlinear expectations
• Three series theorem for independent random variables under sub-linear expectations with applications
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• A strong law of large numbers for non-additive probabilities

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