A unifying view on some problems in probability and statistics

被引：4

作者：

Berti, Patrizia ^{[1
]}

Pratelli, Luca ^{[2
]}

Rigo, Pietro ^{[3
]}

机构：

[1] Univ Modena & Reggio Emilia, Dipartimento Matemat Pura & Applicata G Vitali, I-41100 Modena, Italy

[2] Acad Navale, I-57100 Livorno, Italy

[3] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

来源：

STATISTICAL METHODS AND APPLICATIONS | 2014年 / 23卷 / 04期

关键词：

Compatibility of conditional distributions; De Finetti's coherence principle; Equivalent martingale measure; Equivalent probability measure with given marginals; Finitely additive probability; Fundamental theorem of asset pricing; EXISTENCE; THEOREM;

D O I：

10.1007/s10260-014-0272-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let L be a linear space of real random variables on the measurable space (Omega, A). Conditions for the existence of a probability P on A such that E-P vertical bar X vertical bar < infinity and E-P(X) = 0 for all X is an element of L are provided. Such a P may be finitely additive or sigma-additive, depending on the problem at hand, and may also be requested to satisfy P similar to P-0 or P << P-0 where P-0 is a reference measure. As a motivation, we note that a plenty of significant issues reduce to the existence of a probability P as above. Among them, we mention de Finetti's coherence principle, equivalent martingale measures, equivalent measures with given marginals, stationary and reversible Markov chains, and compatibility of conditional distributions.

引用

页码：483 / 500

页数：18