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Lipschitz continuity of the Wasserstein projections in the convex order on the line

Authors
  • Jourdain, Benjamin
  • Margheriti, William
  • Pammer, Gudmund
Publication Date
Sep 04, 2022
Source
HAL-Ecole des Ponts ParisTech
Keywords
Language
English
License
Unknown
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Abstract

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. Our main result is that, contrary to the minimum and maximum in the convex order, the Wasserstein projections are Lipschitz continuity w.r.t. the Wasserstein distance in dimension one. Moreover, we provide examples that show sharpness of the obtained bounds for the 1-Wasserstein distance.

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