Moment bounds for IID sequences under sublinear expectations  

作　　者：HU Feng1,2 1Department of Mathematics,Qufu Normal University,Qufu 273165,China 2School of Mathematics,Shandong University,Jinan 250100,China 

出　　处：《Science China Mathematics》2011年第10期2155-2160,共6页中国科学：数学（英文版）

基　　金：supported in part by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901);the Natural Science Foundation of Shandong Province (Grant No. ZR2009AL015)

摘　　要：With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.With the notion of independent identically distributed （IID） random variables under sublinear expectations introduced by Peng, we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality, we get the following result： For any continuous function φ satisfying the growth condition ｜φ（x）｜≤ C（1＋ ｜x｜p） for some C 〉 0, p≥ 1 depending on φ, the central limit theorem under sublinear expectations obtained by Peng still holds.

关 键 词：moment bound sublinear expectation IID random variables G-normal distribution central limit theorem 

分 类 号：O211.67[理学—概率论与数理统计]