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 …

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 investigate a mean field optimal control problem obtained in the limit of the optimal
control of large particle systems with forcing and terminal data which are not assumed to be …

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 an extended mean field game the vector field governing the flow of the population can be
different from that of the individual player at some mean field equilibrium. This new class …

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with
common noises and their corresponding $ N $-player games. The theory of mean field game …

This paper studies the convergence of mean field games (MFGs) with finite state space to
MFGs with a continuous state space. We examine a space discretization of a diffusive …

In this manuscript we construct global in time classical solutions to mean field games master
equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include …

In this manuscript we derive a new nonlinear transport equation written on the space of
probability measures that allows to study a class of deterministic mean field games and …