Abstract: Coupling methods provide with a powerful toolbox  for  analysing the long time behaviour of Markov processes. In particular coupling by reflection allows to establish sharp exponential convergence results in Wasserstein distance for the Fokker-Planck equation without having to rely on pointwise assumptions on the confinement potential. The purpose of this talk is to  illustrate the construction of a variant of coupling by reflection that applies to possibly mean-field controlled diffusion processes and yields uniform in time gradient (and Hessian) estimates for the solution of the corresponding Hamilton-Jacobi-Bellman equations. In turn, these estimates are shown to be key to prove various kind of exponential turnpike properties for the optimal processes and controls.

For further information, please write to: elisur.magrini@unibocconi.it