A strong law of large numbers for non-additive probabilities

被引：108

作者：

Chen, Zengjing ^{[1
,2
]}

Wu, Panyu ^{[1
]}

Li, Baoming ^{[3
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Ajou Univ, Dept Financial Engn, Suwon 443749, South Korea

[3] Tsinghua Univ, Sch Publ Policy & Management, Beijing 100084, Peoples R China

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2013年 / 54卷 / 03期

关键词：

Non-additive probability; Strong law of large numbers; Independence; Upper expectation; Bernoulli experiment; STOCHASTIC CALCULUS; EXPECTED UTILITY; BROWNIAN-MOTION; LIMIT-THEOREM; CAPACITIES; AMBIGUITY;

D O I：

10.1016/j.ijar.2012.06.002

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, with the notion of independence for random variables under upper expectations, we derive a strong law of large numbers for non-additive probabilities. This result is a natural extension of the classical Kolmogorov's strong law of large numbers to the case where the probability is no longer additive. As an application of our result, we give most frequent interpretation for Bernoulli-type experiments with ambiguity. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：365 / 377

页数：13

共 24 条

[1]

Chen ZJ, 2011, ADV INTEL SOFT COMPU, V100, P19

[2] Ambiguity, risk, and asset returns in continuous time [J].

Chen, ZJ ;

Epstein, L .

ECONOMETRICA, 2002, 70 (04) :1403-1443

[3]

Cooman G, 2008, ARTIF INTELL, V172, P1400

[4] Weak and strong laws of large numbers for coherent lower previsions [J].

De Cooman, Gert ;

Miranda, Enrique .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2008, 138 (08) :2409-2432

[5] Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths [J].

Denis, Laurent ;

Hu, Mingshang ;

Peng, Shige .

POTENTIAL ANALYSIS, 2011, 34 (02) :139-161

[6]

Dow J., 1993, EC WORKING PAPERS EN, V226

[7] IID: independently and indistinguishably distributed [J].

Epstein, LG ;

Schneider, M .

JOURNAL OF ECONOMIC THEORY, 2003, 113 (01) :32-50

[8]

Feller W., 1968, INTRO PROBABILITY TH

[9]

Feynman R, 1963, QUANTUM MECH, P1

[10]

GILBOA I, 1987, J MATH ECON, V16, P65, DOI 10.1016/0304-4068(87)90022-X

← 1 2 3 →