Geodesics for a class of distances in the space of probability measures

Abstract : In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the existence of a potential function and then give necessary and suffi cient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves.


https://hal.archives-ouvertes.fr/hal-00686908
Contributeur : Bruno Nazaret <>
Soumis le : mercredi 11 avril 2012 - 15:55:54
Dernière modification le : mercredi 28 septembre 2016 - 16:01:27
Document(s) archivé(s) le : jeudi 12 juillet 2012 - 10:00:08

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  • HAL Id : hal-00686908, version 1
  • ARXIV : 1204.2517

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Pierre Cardaliaguet, Guillaume Carlier, Bruno Nazaret. Geodesics for a class of distances in the space of probability measures. 2012. <hal-00686908>

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