This was part of Distributed Solutions to Complex Societal Problems Reunion Workshop
Viscosity Solutions for McKean-Vlasov Control on a torus
Mete Soner, Princeton University
Tuesday, February 21, 2023
Abstract: We consider the viscosity solutions of the dynamic programming equations of a McKean Vlasov control defined using the intrinsic linear derivative. We obtain a comparison result between the Lipschitz viscosity sub and super solutions under a structural assumption on the control set together with the given functions. Proof follows the classical variable doubling argument of Crandall & Lions by using a novel smooth Fourier-Wasserstein metric that we construct. The value function is also shown to be Lipschitz continuous with respect to this metric. This is joint work with Qinxin Yan of Princeton University.