Euler-Maruyama method for distribution dependent stochastic differential equation driven by multiplicative fractional Brownian motion

TL;DR

This paper develops an Euler-Maruyama numerical scheme for distribution-dependent stochastic differential equations driven by multiplicative fractional Brownian motion, providing error bounds and validating results through simulations.

Contribution

It introduces a novel Euler-Maruyama method for DDSDEs with fractional Brownian motion and establishes error bounds with numerical validation.

Findings

Error bounds for the Euler-Maruyama method are derived.

Numerical simulations confirm the theoretical error estimates.

The method effectively approximates solutions of DDSDEs driven by fractional Brownian motion.

Abstract

In this paper, we establish the propagation of chaos and Euler-Maruyama method of DDSDE driven by multiplicative fractional Brownian motion with Hurst parameter $H\in (\frac{\sqrt{5}-1}{2},1)$. We have not only obtained an upper bound for the error of the Euler-Maruyama method but also verified the correctness of this result via systematic numerical simulation experiments.