文献类型：期刊文献

中文题名：容度下的条件期望

英文题名：Conditional Expectation under Capacity

作者：王洪霞[1,2]

第一作者：王洪霞

机构：[1]河南财经政法大学统计学院;[2]河南省教育统计数据分析与研究中心

第一机构：河南财经政法大学统计与大数据学院

年份：2016

卷号：30

期号：3

起止页码：43-50

中文期刊名：模糊系统与数学

外文期刊名：Fuzzy Systems and Mathematics

收录：CSTPCD;;北大核心:【北大核心2014】；CSCD:【CSCD2015_2016】；

基金：河南财经政法大学重大科研基金资助项目(855006);河南省高等学校重点科研项目(15B110002)

语种：中文

中文关键词：条件期望;凹容度;不等式

外文关键词：Conditional Expectation; Concave Capacity; Inequation

摘要：本文研究了客度下的条件期望。首先,在凹容度下给出了条件期望的定义,得出其具有正时齐性、转移不变性、非对称性、次可加性和单调性;接着,证明了其仍然满足C,不等式、Jensen不等式、Hlder不等式和Minkowski不等式。
In this paper, we study about the conditional expectation under the capacity. Firstly, we introduce the concept of conditional Choquet expectation which is the conditional expectation with respect to concave capacity, and then we prove some properties of this concept, which include positive homogeneity, translation invariance, asymmetry, subadditivity and monotonicity. Then, we state that Cr inequality, Schwarz inequality, Holder＇ s inequality, Minkowski inequality and Jensen＇ s inequality still hold for this kind of conditional expectations.