Characterization of set-valued conditional expectation

被引：3

作者：

Zohry, M. ^{[1
]}

机构：

[1] Univ Abdelmalek Essadi, Dept Math, Tatouan, Morocco

来源：

MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 12期

关键词：

set-valued random variable; set-valued integral; conditional expectation; integrand;

D O I：

10.1002/mana.200410426

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an essentially bounded closed-convex-nonempty set-valued random variable, it is shown that the conditional expectation is characterized by its integrals over the sets of the associated sigma-field. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1376 / 1382

页数：7

共 26 条

[1] INTEGRALS OF SET-VALUED FUNCTIONS
AUMANN, RJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1965, 12 (01) : 1 - &
[2] CONVEX INTEGRANDS AND PROBABILITIES
BISMUT, JM
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1973, 42 (03) : 639 - 673
[3] CASTAING C, 1967, REV FR INFORM RECH O, V1, P91
[4] A NOTE ON THE CONVERGENCE OF BANACH-SPACE VALUED MARTINGALES
CHATTERJI, SD
[J]. MATHEMATISCHE ANNALEN, 1964, 153 (02) : 142 - 149
[5] MARTINGALE CONVERGENCE AND RADON-NIKODYM THEOREM IN BANACH SPACES
CHATTERJI, SD
[J]. MATHEMATICA SCANDINAVICA, 1968, 22 (01) : 21 - +
[6] CHATTERJI SD, 1960, B AM MATH SOC, V66, P395, DOI [DOI 10.1090/S0002-9904-1960-10471-5, 10.1090/S0002-9904-1960-10471-5]
[7] Choirat C, 2003, ANN PROBAB, V31, P63
[8] DEBREU G, 1967, CONTRIBUTIONS PROB 1, V2, P351
[9] EZZAKI F, 1996, B POL ACAD SCI MATH, V0044, P00353
[10] INTEGRALS, CONDITIONAL EXPECTATIONS, AND MARTINGALES OF MULTIVALUED FUNCTIONS
HIAI, F
UMEGAKI, H
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1977, 7 (01) : 149 - 182

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