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

TL;DR

This paper studies the strong convergence of a neutral McKean-Vlasov SDE with super-linear delay driven by fractional Brownian motion, establishing existence, uniqueness, moment bounds, propagation of chaos, and numerical convergence.

Contribution

It introduces a new analysis of the Euler-Maruyama scheme for nonlinear delayed McKean-Vlasov SDEs driven by fractional Brownian motion, including convergence rates.

Findings

Existence and uniqueness of solutions are established.

The Euler-Maruyama scheme converges strongly to the exact solution.

Numerical examples validate the theoretical results.

Abstract

In this paper, our main aim is to investigate 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 converges strongly to the exact solution. Furthermore, a corresponding numerical example is given to illustrate the theory.