Geodesics for a class of distances in the space of probability measures
Optimization and Control
2012-04-12 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1204.2517,
title = {Geodesics for a class of distances in the space of probability measures},
author = {Pierre Cardaliaguet and Guillaume Carlier and Bruno Nazaret},
journal= {arXiv preprint arXiv:1204.2517},
year = {2012}
}