Some Inequalities and Limit Theorems Under Sublinear Expectations  

作　　者：Ze-Chun HU Yan-Zhi YANG 

机构地区：[1]College of Mathematics, Sichuan University [2]Department of Mathematics, Nanjigng University

出　　处：《Acta Mathematicae Applicatae Sinica》2017年第2期451-462,共12页应用数学学报（英文版）

基　　金：Supported in part by the National Natural Science Foundation of China under Grant No.11371191;Jiangsu Province Basic Research Program(Natural Science Foundation)under Grant No.BK2012720

摘　　要：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.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.

关 键 词：sublinear expectation INEQUALITY the law of large numbers SUBMARTINGALE 

分 类 号：O211[理学—概率论与数理统计]