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

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

2012-04-11

arxiv.org/abs/1204.2517v1

Mathematics

Optimization and Control

Scientific paper

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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