Existence of solutions for mean-field integrodifferential equations with delay

Abstract

In this paper, we study the existence and continuous dependence on coefficients of mild solutions for first-order McKean–Vlasov integrodifferential equations with delay driven by a cylindrical Wiener process using resolvent operator theory and Wasserstein distance. Under the situation that the nonlinear term depends on the probability distribution of the state, the existence and uniqueness of solutions are established. An example illustrating the general results is included.