Convergences of Random Variables Under Sublinear Expectations  

作　　者：Zechun HU Qianqian ZHOU 

机构地区：[1]College of Mathematics, Sichuan University [2]School of Mathematical Sciences, Nankai University [3]Department of Mathematics, Nanjing University

出　　处：《Chinese Annals of Mathematics,Series B》2019年第1期39-54,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11771309);the Fundamental Research Funds for the Central Universities of China

摘　　要：In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution,and give some equivalent characterizations of convergence in distribution. In addition,they give a dominated convergence theorem under sublinear expectations, which may have its own interest.In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution,and give some equivalent characterizations of convergence in distribution. In addition,they give a dominated convergence theorem under sublinear expectations, which may have its own interest.

关 键 词：SUBLINEAR EXPECTATION Capacity The dominated CONVERGENCE THEOREM 

分 类 号：O1[理学—数学]