Irreducible convex paving for decomposition of multidimensional martingale transport plans

By H. D. March, Nizar Touzi. Annals of Probability, 2017

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/24b36ae9d2f29c15cf8184f1e5922efb722e30cb

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Structure of optimal martingale transport plans in general dimensions (2015, background): “We refer to [12], [28] for some relevant progress in this direction.”
Martingale Benamou–Brenier: A probabilistic perspective (2017, methodology): “We conjecture that a similar structural characterization of sBm can be established in general dimensions, pending future developments in the direction of [21, 48].”