Three series theorem for independent random variables under sub-linear expectations with applications

DOI10.1007/s10114-018-7508-9zbMath1411.60046arXiv1712.08279OpenAlexW2964280749WikidataQ129002929 ScholiaQ129002929MaRDI QIDQ1734914

Xianqiang Yang

Publication date: 27 March 2019

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

Full work available at URL: https://arxiv.org/abs/1712.08279

zbMATH Keywords

capacitysub-linear expectationRosenthal inequalityKolmogorov's three series theoremMarcinkiewicz's strong law of large numbers

Mathematics Subject Classification ID

Strong limit theorems (60F15)

Related Items (14)

Several different types of convergence for ND random variables under sublinear expectations ⋮ NOTE ON STRONG LAW OF LARGE NUMBER UNDER SUB-LINEAR EXPECTATION ⋮ Note on precise rates in the law of iterated logarithm for the moment convergence of i.i.d.: random variables under sublinear expectations ⋮ Convergence of linear processes generated by negatively dependent random variables under sub-linear expectations ⋮ Equivalent conditions of complete convergence and Marcinkiewicz-Zygmund-type strong law of large numbers for i.i.d. sequences under sub-linear expectations ⋮ Complete and Complete Integral Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables under Sublinear Expectations ⋮ Limit theorems for delayed sums under sublinear expectation ⋮ Central limit theorem for linear processes generated by m-dependent random variables under the sub-linear expectation ⋮ Unnamed Item ⋮ The convergence of the sums of independent random variables under the sub-linear expectations ⋮ Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation ⋮ Equivalent conditions of complete \(p\)th moment convergence for weighted sums of i. i. d. random variables under sublinear expectations ⋮ Theorems of complete convergence and complete integral convergence for END random variables under sub-linear expectations ⋮ Unnamed Item

Cites Work

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• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation

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