An explicit Euler method for McKean-Vlasov SDEs driven by fractional Brownian motion

TL;DR

This paper develops a theoretical framework and numerical scheme for McKean-Vlasov SDEs driven by fractional Brownian motion, including error bounds and numerical validation.

Contribution

It introduces an Euler-Maruyama scheme for these equations and establishes chaos propagation theory with error estimates.

Findings

Error bounds for the Euler scheme are derived.

Numerical experiments confirm theoretical predictions.

Chaos propagation is rigorously established.

Abstract

In this paper, we establish the theory of chaos propagation and propose an Euler-Maruyama scheme for McKean-Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst exponent $H \in (0,1)$. Meanwhile, upper bounds for errors in the Euler method is obtained. A numerical example is demonstrated to verify the theoretical results.