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.
Document type :
Preprints, Working Papers, ...
2012


https://hal.archives-ouvertes.fr/hal-00686908
Contributor : Bruno Nazaret <>
Submitted on : Wednesday, April 11, 2012 - 3:55:54 PM
Last modification on : Wednesday, April 11, 2012 - 8:31:45 PM

Files

duality-opticond-HAL.pdf
fileSource_public_author

Identifiers

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

Collections

Citation

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

Export

Share

Metrics

Consultation de
la notice

126

Téléchargement du document

43