Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

Abstract

As extensions to the corresponding results derived for time homogeneous McKean-Vlasov SDEs, the exponential ergodicity is proved for time-periodic distribution dependent SDEs in three different situations:

1) in the quadratic Wasserstein distance and relative entropy for the dissipative case;

2) in the Wasserstein distance induced by a cost function for the partially dissipative case; and

3) in the weighted Wasserstein distance induced by a cost function and a Lyapunov function for the fully non-dissipative case.

The main results are illustrated by time inhomogeneous granular media equations, and are extended to reflecting McKean-Vlasov SDEs in a convex domain.