Irreducible convex paving for decomposition of multidimensional martingale transport plans
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Publication:2421828
DOI10.1214/18-AOP1295zbMATH Open1467.60028arXiv1702.08298WikidataQ127930847 ScholiaQ127930847MaRDI QIDQ2421828
Publication date: 18 June 2019
Published in: The Annals of Probability (Search for Journal in Brave)
Abstract: Martingale transport plans on the line are known from Beiglbock & Juillet 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 R^d, d larger than one. Our decomposition is a partition of 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.
Full work available at URL: https://arxiv.org/abs/1702.08298
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