Strong laws of large numbers for sub-linear expectations  

作　　者：CHEN ZengJing 

机构地区：[1]School of Mathematics, Shandong University

出　　处：《Science China Mathematics》2016年第5期945-954,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11231005)

摘　　要：We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed（IID） random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov＇s strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.

关 键 词：capacity strong law of large numbers independently and identically distributed nonlinear expectation 

分 类 号：O211.4[理学—概率论与数理统计]