5 papers
Rearranged Stochastic Heat Equations with an Entropy Gradient Structure
Francois Delarue, Rhoss Likibi Pellat
We extend a previously introduced one-dimensional diffusion model on the space of probability measures, defined via the rearranged stochastic heat equation by, penalizing the dynam…
Major-minor mean field games: common noise helps
Francois Delarue, Chenchen Mou
The objective of this work is to study the existence, uniqueness, and stability of equilibria in mean field games involving a major player and a continuum of minor players over fin…
Itô's Formula for the Rearranged Stochastic Heat Equation
François Delarue, William R. P. Hammersley
The purpose of this short note is to prove a convenient version of Itô's formula for the Rearranged Stochastic Heat Equation (RSHE) introduced by the two authors in a previous cont…
Fourier Galerkin approximation of mean field control problems
François Delarue, Mattia Martini
The purpose of this work is to provide a finite dimensional approximation of the solution to a mean field optimal control problem set on the -dimensional torus. The approximatio…
Propagation of chaos for mean field rough differential equations
I. Bailleul, R. Catellier, F. Delarue
We address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type $$ dX_t = V(X_t,\mathcal{L}…