Characterization of a class of weak transport-entropy inequalities on the line

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, pp. 1667-1693, 2018.

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Abstract:

We study an weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost function. As an application, we give a necessary and sufficient condition for weak transport-entropy inequalities ...More

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