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May 2019 Irreducible convex paving for decomposition of multidimensional martingale transport plans
Hadrien De March, Nizar Touzi
Ann. Probab. 47(3): 1726-1774 (May 2019). DOI: 10.1214/18-AOP1295

Abstract

Martingale transport plans on the line are known from Beiglböck and Juillet (Ann. Probab. 44 (2016) 42–106) to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in $\mathbb{R}^{d}$, $d\ge1$. Our decomposition is a partition of $\mathbb{R}^{d}$ consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well defined. We justify the relevance of our decomposition by proving the existence of a martingale transport plan filling these components. We also deduce from this decomposition a characterization of the structure of polar sets with respect to all martingale transport plans.

Citation

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Hadrien De March. Nizar Touzi. "Irreducible convex paving for decomposition of multidimensional martingale transport plans." Ann. Probab. 47 (3) 1726 - 1774, May 2019. https://doi.org/10.1214/18-AOP1295

Information

Received: 1 March 2017; Revised: 1 June 2018; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067281
MathSciNet: MR3945758
Digital Object Identifier: 10.1214/18-AOP1295

Subjects:
Primary: 60G42
Secondary: 49N05

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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