基于加权g-期望的Jensen不等式,矩不等式与大数定律  

Jensen's inequality,moment inequality and law of large numbers for weighted g-expectation

作　　者：江龙[1] 陈敏[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《山东大学学报（理学版）》2016年第8期1-9,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11371362)

摘　　要：在g-期望的基础上提出加权g-期望ελg[·]的概念。证明了当生成元g关于y非增且关于(y,z)满足正齐次性时,基于加权g-期望的矩不等式一般成立。在λ≥12且生成元g不依赖于y的条件下,在g关于z满足超齐次性时,建立了基于加权g-期望的Jensen不等式;当g关于z满足次线性时,建立了基于加权g-期望的大数定律。We propose the notion of weighted g-expectationελg [·]based on g-expectation.We prove that if the gener-ator g is non-increasing with respect to y and positive-homogeneous with respect to (y,z),the moment inequality for weighted g-expectation holds in general.Whenλ≥ 12 and the generator g is independent of y,we establish Jensen’s in-equality for weighted g-expectation when g is super-homogeneous with respect to z,and we establish the law of large numbers for weighted g-expectation when g is sublinear with respect to z.

关 键 词：G-期望 加权g-期望 JENSEN不等式 矩不等式 大数定律 

分 类 号：O211[理学—概率论与数理统计]