Mckean-Vlasov stochastic differential equations in Hilbert spaces under Caratheodory conditions

Abstract

We establish results concerning the global existence, uniqueness, and controllability of mild solutions for a class of first-order abstract McKean-Vlasov stochastic evolution Equations with variable delay in a real separable Hilbert space. We allow the nonlinearities at a given time t to depend on the probability distribution at time t corresponding to the solution at time t. The results are obtained by imposing a so-called Caratheodory condition on the nonlinearities, which is weaker than the classical Lipschitz condition. Examples illustrating the applicability of the general theory are also provided.