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August 2019 Stochastic monotonicity from an Eulerian viewpoint
Davide Gabrielli, Ida Germana Minelli
Braz. J. Probab. Stat. 33(3): 558-585 (August 2019). DOI: 10.1214/18-BJPS403

Abstract

Stochastic monotonicity is a well-known partial order relation between probability measures defined on the same partially ordered set. Strassen theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of finitely decomposable flows on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having divergence given by the difference of the two measures. We illustrate the result with some examples.

Citation

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Davide Gabrielli. Ida Germana Minelli. "Stochastic monotonicity from an Eulerian viewpoint." Braz. J. Probab. Stat. 33 (3) 558 - 585, August 2019. https://doi.org/10.1214/18-BJPS403

Information

Received: 1 July 2017; Accepted: 1 May 2018; Published: August 2019
First available in Project Euclid: 10 June 2019

zbMATH: 07094818
MathSciNet: MR3960277
Digital Object Identifier: 10.1214/18-BJPS403

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 3 • August 2019
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