Existence of entrance measures for time-inhomogeneous McKean-Vlasov SDEs is shown in great generality, with periodic and asymptotic quasi-periodic measures obtained through a double-lifted dynamical system on the cylinder yielding an invariant measure for the lifted semigroup.
Kac , Foundations of kinetic theory , in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol
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Entrance measures and dynamics for time-inhomogeneous McKean-Vlasov stochastic differential equations
Existence of entrance measures for time-inhomogeneous McKean-Vlasov SDEs is shown in great generality, with periodic and asymptotic quasi-periodic measures obtained through a double-lifted dynamical system on the cylinder yielding an invariant measure for the lifted semigroup.