The stochastic order of probability measures on ordered metric spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Hiai, Fumio¹  Lawson, Jimmie²  Lim, Yongdo³ 

[1] Tohoku Univ, Hakusan 3-8-16-303, Abiko, Chiba 2701154, Japan

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[3] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

关键词: Stochastic order;    Borel probability measure;    Ordered metric space;    Normal cone;    Wasserstein metric;    AGH mean inequalities;   

DOI  :  10.1016/j.jmaa.2018.04.038

来源: Elsevier

【 摘 要 】

The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of probability measures on ordered Banach spaces, we introduce and study a stochastic order on the space of probability measures P(X), where X is a metric space equipped with a closed partial order, and derive several useful equivalent versions of the definition. We establish the antisymmetry and closedness of the stochastic order (and hence that it is a closed partial order) for the case of a partial order on a Banach space induced by a closed normal cone with interior. We also consider order-completeness of the stochastic order for a cone of a finite-dimensional Banach space and derive a version of the arithmetic-geometric-harmonic mean inequalities in the setting of the associated probability space on positive invertible operators on a Hilbert space. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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