Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications  

作　　者：Jia Pan XU Li Xin ZHANG 

机构地区：[1]School of Mathematical Sciences, Zhejiang University

出　　处：《Acta Mathematica Sinica,English Series》2019年第2期172-184,共13页数学学报（英文版）

基　　金：Supported by the NSF of China(Grant No.11731012);the 973 Program(Grant No.2015CB352302);Zhejiang Provincial Natural Science Foundation(Grant No.LY17A010016);the Fundamental Research Funds for the Central Universities

摘　　要：In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.

关 键 词：Sub-linear EXPECTATION capacity Rosenthal's INEQUALITY Kolmogorov's three series theorem Marcinkiewicz's strong law of large numbers 

分 类 号：O1[理学—数学]