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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We acknowledge the helpful suggestions and comments of an anonymous referee, which improved the presentation of this paper.
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Supported in part by the National Natural Science Foundation of China under Grant No. 11371191 and Jiangsu Province Basic Research Program (Natural Science Foundation) under Grant No. BK2012720.
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Hu, ZC., Yang, YZ. Some inequalities and limit theorems under sublinear expectations. Acta Math. Appl. Sin. Engl. Ser. 33, 451–462 (2017). https://doi.org/10.1007/s10255-017-0673-2
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DOI: https://doi.org/10.1007/s10255-017-0673-2