基于加权g-期望的Jensen不等式,矩不等式与大数定律

doi:10.6040/j.issn.1671-9352.0.2016.312

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (8): 1-9.doi: 10.6040/j.issn.1671-9352.0.2016.312

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基于加权g-期望的Jensen不等式,矩不等式与大数定律

江龙,陈敏

中国矿业大学理学院, 江苏徐州 221116

收稿日期:2016-06-29 出版日期:2016-08-20 发布日期:2016-08-08
作者简介:江龙(1964— ), 男, 博士, 教授, 研究方向为倒向随机微分方程与非线性数学期望. E-mail:jianglong365@hotmail.com
基金资助:
国家自然科学基金资助项目(11371362)

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

JIANG Long, CHEN Min

College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received:2016-06-29 Online:2016-08-20 Published:2016-08-08

摘要/Abstract

摘要： 在g-期望的基础上提出加权g-期望ε^λ_g ［·］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≥1/2 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。

关键词: g-期望, Jensen不等式, 大数定律, 矩不等式, 加权g-期望

Abstract: We propose the notion of weighted g-expectation ε^λ_g ［·］ based on g-expectation. We prove that if the generator 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. When λ≥1/2 and the generator g is independent of y, we establish Jensens inequality 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.

Key words: weighted g-expectation, Jensens inequality, law of large numbers, g-expectation, moment inequality

中图分类号:

O211

江龙,陈敏. 基于加权g-期望的Jensen不等式,矩不等式与大数定律[J]. 山东大学学报（理学版）, 2016, 51(8): 1-9.

JIANG Long, CHEN Min. Jensens inequality, moment inequality and law of large numbers for weighted g-expectation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 1-9.

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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

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