paper
Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
Guillaume Carlier, Alex Delalande, Quentin Mérigot
Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
Guillaume Carlier, Alex Delalande, Quentin Mérigot
Paper2024-01-02English
quantitative financearxiv
Description
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight Hölder-behavior for this operation under minimal assumptions. Our proof essentially relies on a new bound that quantifies the size of the singular sets of a convex and Lipschitz continuous function on a bounded domain.
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