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

Jiapan Xu; Lixin Zhang

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arXiv · 1712.08279

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

Jiapan Xu·Lixin Zhang

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Abstract

In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we give a theorem about the convergence of a random series and establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.

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Jiapan Xu, Lixin Zhang. 2017-12-22. Three series theorem for independent random variables under sub-linear expectations with applications. https://arxiv.org/abs/1712.08279

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