Existence of invariant probability measures for functional McKean-Vlasov SDEs

We show existence of an invariant probability measure for a class functional McKean-Vlasov SDEs by applying Kakutani’s fixed point theorem to suitable measures on space continuous functions. Unlike some previous works [1, 25], we do not assume monotonicity condition hold. Further, our conditions are even weaker than results in the literature without dependence law solution [12].