Some inequalities and limit theorems under sublinear expectations

Ze-Chun Hu, Yan-Zhi Yang

Published 2012-07-02, updated 2014-08-28Version 3

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.