A Tikhonov Theorem for McKean Vlasov SDEs and an application to mean-field control problems.
We present a stochastic Tikhonov theorem for two-scales systems of SDEs, which cover the case of McKean-Vlasov SDEs. Our approach extends and generalizes previous results on two-scales systems of SDEs without mean-field interaction. As an application we provide a novel method for approximating the solution of certain systems of FBSDEs, related to the Pontryagin maximum principle, which is new even for the case without mean-field interaction. This is a joint work with A. Cosso.