集值极限鞅的Riesz逼近及其收敛性

集值极限鞅的Riesz逼近及其收敛性

李高明¹, 赵辉²

1. 武警工程学院数学教研室, 西安 710086; 2. 陕西师范大学民族教育研究中心, 西安 710062

收稿日期:2006-12-18 修回日期:1900-01-01 出版日期:2007-09-26 发布日期:2007-09-26
通讯作者: 李高明

Riesz Approximation of Setvalued Martingale in the Limit and Its Convergence

LI Gaoming¹, ZHAO Hui²

1. Department of Mathematics, Engineering College of Armed Police Force, Xi’an 710086, China; 2. Education Research Center of Minority Nationality, Shaanxi Normal University, Xi’an 710062, China

Received:2006-12-18 Revised:1900-01-01 Online:2007-09-26 Published:2007-09-26
Contact: LI Gaoming

摘要/Abstract

摘要： 假设（X,||·||）为可分的Banach空间, X^*为其对偶空间. 设(Ω,B,P)为完备的概率空间, {B_n, n≥1}为B的上升子σ-域族, 且B=∨B_n. 证明了集值极限鞅的Riesz逼近定理, 并在此基础上, 给出了集值极限鞅在KuratowskiMosco收敛意义、 Kuratowski收敛意义及弱收敛意义下的收敛定理.

关键词: 集值极限鞅, Riesz逼近, KuratowskiMosco收敛, Kuratowski收敛, 弱收敛

Abstract: Let （X,‖·‖） be a real separable Banach space with the dual X^*, (Ω, B ,P) be a complete probability s pace, further, {B_n, n≥1} be a increase sub σ-fields filtration of B , and B=∨B_n, we proved the Riesz approximation theorem of setvalued martingales in the limit, and made use of the results present the convergence theorenm of setvalued martingales in the limit.

Key words: setvalued martingales in the limit, Riesz approxim ation theorem, KuratowskiMosco convergence, Kuratowski convergence, weak convergence

中图分类号:

O211.6

李高明, 赵辉. 集值极限鞅的Riesz逼近及其收敛性[J]. J4, 2007, 45(05): 713-716.

LI Gaoming, ZHAO Hui. Riesz Approximation of Setvalued Martingale in the Limit and Its Convergence[J]. J4, 2007, 45(05): 713-716.

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