文献类型：期刊文献

英文题名：Conditional Choquet Expectation

作者：Wang, Hongxia[1]

第一作者：王洪霞

通讯作者：Wang, HX[1]

机构：[1]Henan Univ Econ & Law, Coll Stat, Zhengzhou 450002, Henan, Peoples R China

第一机构：河南财经政法大学统计与大数据学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Coll Stat, Zhengzhou 450002, Henan, Peoples R China.|[1048415]河南财经政法大学统计与大数据学院;[10484]河南财经政法大学;

年份：2015

卷号：44

期号：18

起止页码：3782-3795

外文期刊名：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

收录：;EI(收录号：20153801296082);Scopus(收录号：2-s2.0-84942031493);WOS:【SCI-EXPANDED(收录号:WOS:000362340800002)】；

基金：This article is supported by Scientific Research Foundation for Doctors, Henan University of Economics and Law.

语种：英文

外文关键词：Conditional Choquet expectation; Conditional capacity; Inequality; Submodular capacity

摘要：Capacity plays an important role in many areas. A capacity is usually studied under the assumption that it is submodular. In this article, we first present several inequalities for the submodular capacity and state some special submodular capacities. Second, we introduce the concept of conditional Choquet expectation which is the conditional expectation with respect to submodular capacity, and then we prove some properties of this concept, which include positive homogeneity, translation invariance, asymmetry, subadditivity, and monotonicity. Finally, we state that C-r inequality, Schwarz inequality, Holder's inequality, Minkowski inequality, and Jensen's inequality still hold for this kind of conditional Choquet expectations.