次线性期望下的若干矩不等式  

Several Moment Inequalities under Sublinear Expectations

作　　者：兰玉婷 张宁 LAN YUTING,ZHANG NING(1.School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;2.School of Mathematics, Shandong University, Jinan 250100, Chin)

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]山东大学数学学院,济南250100

出　　处：《应用数学学报》2018年第2期229-248,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金青年项目(11601280)资助

摘　　要：本文在Peng建立的次线性期望空间下证明了Bernstein不等式，Kolmogorov不等式以及Rademacher不等式．进一步，本文分别应用Bernstein不等式、Kolmogorov不等式以及Rademacher不等式对次线性期望空间下随机变量列的拟必然收敛性质进行了深入研究，并得到了相应的强收敛定理．In this paper, a Bernstein inequality, a Kolmogorov inequality and a Rademacher inequality are established under sublinear expectations introduced by Peng. Then, as applications of those inequalities, the quasi sure convergence of random variables under sublinear expectations is investigated and several strong limit theorems are obtained.

关 键 词：次线性期望 独立随机变量 BERNSTEIN不等式 Kolmogorov不等式 Rademacher不等式 

分 类 号：O211.4[理学—概率论与数理统计] O211.5[理学—数学]