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arXiv · 1204.2517

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

Pierre Cardaliaguet·Guillaume Carlier·Bruno Nazaret
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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.

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Pierre Cardaliaguet, Guillaume Carlier, Bruno Nazaret. 2012-04-11. Geodesics for a class of distances in the space of probability measures. https://arxiv.org/abs/1204.2517

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