On the convergence of caratheodory numerical scheme for Mckean-Vlasov equations

We study the strong convergence of the Caratheodory numerical scheme for a class of nonlinear McKean-Vlasov stochastic differential equations (MVSDE). We prove, under Lipschitz assumptions, the convergence of the approximate solutions to the unique solution of the MVSDE. Moreover, we show that the result remains valid, under continuous coefficients, provided that pathwise uniqueness holds. The proof is based on weak convergence techniques and the Skorokhod embedding theorem. In particular, this general result allows us to construct the unique strong solution of a MVSDE by using the Caratheodory numerical scheme. Examples under which pathwise uniqueness holds are given.