5 citations · 6 across the 11 of their papers we have counts for
4 papers · 1 filter
Wasserstein spaces have the Radon-Nikodym property
Charles Bertucci
Wasserstein spaces carry two natural geometries: a vertical one, inherited from the linear structure of signed measures, and a horizontal one, induced by couplings. We prove that a…
Analysis on spaces of measures
Charles Bertucci
This work presents analytical tools for studying functions defined on spaces of measures, together with two applications: mean field game master equations and first order Hamilton-…
Infinite horizon stochastic optimal control with sign-changing discount factor
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
We study an infinite horizon stochastic optimal control problem by means of the associated Hamilton-Jacobi-Bellman equation. The problem we are studying has the particularity of ha…
Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces
Charles Bertucci, Pierre-Louis Lions
We present a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on Wasserstein spaces of probability measures over . In addition to the use o…