Strong convergence of Euler–Maruyama schemes for doubly perturbed McKean–Vlasov stochastic differential equations

Abstract

In this paper, we develop strong convergence of the Euler–Maruyama (EM) scheme for approximating the doubly perturbed McKean–Vlasov stochastic differential equations. In contrast to the existing work, a novel feature is that we use more general conditions for parameters α and β. To obtain the desired approximation, this paper also proves the existence and uniqueness of strong solution for this class of McKean–Vlasov SDEs. Combining with the results of propagation of chaos, the overall convergence rate is obtained for the EM scheme. Finally, two numerical examples are provided to demonstrate our results.