The goal of this work is to obtain (nearly) optimal rates for the convergence problem in mean
field control. Our analysis covers cases where the solutions to the limiting problem may not …

An optimal control problem in the space of probability measures and the viscosity solutions
of the corresponding dynamic programming equations defined using the intrinsic linear …

We establish the well-posedness of viscosity solutions for a class of semi-linear Hamilton-
Jacobi equations set on the space of probability measures on the torus. In particular, we …

Dynamic programming equations for mean field control problems with a separable structure
are Eikonal type equations on the Wasserstein space. Standard differentiation using linear …

The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear
Hamilton–Jacobi equations in the space of probability measures. The method involves …

We introduce a stochastic version of the optimal transport problem. We provide an analysis
by means of the study of the associated Hamilton–Jacobi–Bellman equation, which is set on …

In this paper we investigate a path dependent optimal control problem on the process space
with both drift and volatility controls, with possibly degenerate volatility. The dynamic value …

We consider the convergence problem in the setting of mean field control with common
noise and degenerate idiosyncratic noise. Our main results establish a rate of convergence …

This work is the third part of a program initiated in arxiv: 2111.13258, arxiv: 2302.06571
aiming at the development of an intrinsic geometric well-posedness theory for Hamilton …

This work is the second part of a program initiated in arxiv: 2111.13258 aiming at the
development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations …