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Journal articles
KANTOROVICH DUALITY FOR GENERAL TRANSPORT COSTS AND APPLICATIONS
Abstract : We introduce a general notion of transport cost that encompasses many costs used in the literature (including the classical one and weak transport costs introduced by Talagrand and Marton in the 90's), and prove a Kantorovich type duality theorem. As a by-product we obtain various applications in different directions: we give a short proof of a result by Strassen on the existence of a martingale with given marginals, we characterize the associated transport-entropy inequalities together with the log-Sobolev inequality restricted to convex/concave functions. Some explicit examples of discrete measures satisfying weak transport-entropy inequalities are also given.
Cited literature [64 references]
https://hal-upec-upem.archives-ouvertes.fr/hal-01098114
Contributor : Nathael Gozlan Connect in order to contact the contributor
Submitted on : Thursday, December 24, 2015 - 3:01:55 PM
Last modification on : Tuesday, March 2, 2021 - 10:14:39 AM
Long-term archiving on: : Friday, March 25, 2016 - 12:01:06 PM
Contributor : Nathael Gozlan Connect in order to contact the contributor
Submitted on : Thursday, December 24, 2015 - 3:01:55 PM
Last modification on : Tuesday, March 2, 2021 - 10:14:39 AM
Long-term archiving on: : Friday, March 25, 2016 - 12:01:06 PM
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GRST-Duality-cut version.pdf
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