Louis-Pierre Chaintron (ENS Paris)

Stability of constrained Fokker-Planck equations, a mean-field control approach

Fokker-Planck equations are widely used to model physical phenomena, their link with stochastic diffusions being used to account for average effects which need not being specified. However, the proposed model is always an approximation that cannot exactly reproduce all the features of the real system (mean, variance, higher order moment…). When such an inaccuracy is measured, a stochastic control approach can be used to bias the dynamics and select the desired behavior. Starting from and ODE setting, I will present this procedure and its stability properties. I will then turn to PDEs and I will make a link with probability approaches. This work is a collaboration with Giovanni Conforti (University of Padua) and Julien Reygner (CERMICS, ENPC).