集值逆上鞅的Doob分解  

Doob Decomposition for Set-valued Inverse Supermartingle

作　　者：李高明 李海鹏[2] Li Gao-ming;LI Hai-peng(College of Science,Engineering University of the Armed Police Force,Xi'an710086,China;No.1General Department,Xi'an Electronic Engineering Reserch Institute,Xi'an710100,China)

机构地区：[1]武警工程大学院理学院,陕西西安710086 [2]西安电子工程研究所总体一部,陕西西安710100

出　　处：《模糊系统与数学》2018年第5期96-101,共6页Fuzzy Systems and Mathematics

基　　金：武警工程大学基础研究基金资助项目(WJY201408)

摘　　要：假定(X,‖·‖)为可分的Banach空间,X*为其对偶空间,X*可分。本文首先给出了集值逆上鞅Doob分解的概念,其次,证明了实值逆上鞅Doob分解定理,在此基础上,利用支撑函数给出了集值逆上鞅可Doob分解的一个充分必要条件。同时证明了一维实空间R1中集值逆上鞅具有Doob分解,最后,用例子说明在二维实空间R2并非所有的集值逆上鞅都具有Doob分解。Throughout this paper,(X,||.||)will denote be a real separable Banach space with the dual X^*,X^*is separable.First of all,a new definition about Doob decomposition of set-valued inversesupermartingleis presented in this paper.Secondly,we discussed Doob decomposition theorem of realvaluedinversesupermartingale.We alsoprove that theset-valuedinverse supermartingle abtains the new form of definition in one dimension real space.Thirdly,in order,to illustrate that the new definition is not available in two dimensions real space,somes examples are given here.At last,we used support function to prove its the sufficient and necessary conditions of this new Doob decomposition.

关 键 词：集值逆(上)鞅Doob分解 集值可料逆增过程 支撑函数 

分 类 号：O211[理学—概率论与数理统计]