Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations

DOI10.1007/s10114-015-3212-1zbMath1319.60043arXiv1211.1090OpenAlexW1988532004MaRDI QIDQ2355453

Ling Zhou, Ze-Chun Hu

Publication date: 23 July 2015

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

Full work available at URL: https://arxiv.org/abs/1211.1090

zbMATH Keywords

law of large numberscentral limit theoremsublinear expectations

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (8)

Central limit theorems for sub-linear expectation under the Lindeberg condition ⋮ Backward stochastic differential equations with regime-switching and sublinear expectations ⋮ Optimal unbiased estimation for maximal distribution ⋮ Equivalent conditions of complete convergence and Marcinkiewicz-Zygmund-type strong law of large numbers for i.i.d. sequences under sub-linear expectations ⋮ Central limit theorem for linear processes generated by m-dependent random variables under the sub-linear expectation ⋮ Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation ⋮ Central limit theorems for bounded random variables under belief measures ⋮ An \(\alpha\)-stable limit theorem under sublinear expectation

Cites Work

• Central limit theorem for capacities
• A general central limit theorem under sublinear expectations
• Moment bounds for IID sequences under sublinear expectations
• Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• A Weighted Central Limit Theorem Under Sublinear Expectations
• On the regularity theory of fully nonlinear parabolic equations: II

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