Some inequalities and limit theorems under sublinear expectations

Ze-Chun Hu; Yan-Zhi Yang

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arXiv · 1207.0489

Some inequalities and limit theorems under sublinear expectations

Ze-Chun Hu·Yan-Zhi Yang

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Abstract

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.

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Ze-Chun Hu, Yan-Zhi Yang. 2015-06-18. Some inequalities and limit theorems under sublinear expectations. https://arxiv.org/abs/1207.0489

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