Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions

Abstract

The primary objective of this paper is to explore the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent $H\in (1/2,1)$. After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama (EM) scheme and show that the numerical solution convergent to the true solution strongly. Furthermore, a related example is given to illustrate the theory.