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

By Pierre Cardaliaguet, Guillaume Carlier, Bruno Nazaret. Calculus of Variations and Partial Differential Equations, 2012

51 citations recorded by the source corpus.

In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savaré. We first prove the existence of a potential function and then give necessary and sufficient 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.

Subfields: Applied Mathematics, Finance, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/484ce5110173d4e692b39dcb86b59844d2c7f4bb

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Citations in the corpus

Weak Solutions for First Order Mean Field Games with Local Coupling (2013, result): “In fact part of our analysis is close to the one developed in Cardaliaguet, Carlier and Nazaret [10] for a particular optimal transport problem: in particular the notion of weak solution is similar to the one introduced in [10].”
Second order mean field games with degenerate diffusion and local coupling (2014, methodology): “The strategy of proof—which is very close to the corresponding one in [4, 5, 6]—consists in applying the Fenchel-Rockafellar duality theorem (cf.”