Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motion

TL;DR

This paper investigates how quickly Euler approximations converge when solving mixed stochastic differential equations driven by both Brownian and fractional Brownian motions with Hurst parameter greater than 1/2.

Contribution

It provides the mean-square rate of convergence for Euler approximations of solutions to mixed SDEs involving both Brownian and fractional Brownian motions.

Findings

Established the mean-square convergence rate for Euler schemes.

Extended analysis to equations driven by fractional Brownian motion with H>1/2.

Results applicable to numerical solutions of mixed stochastic systems.

Abstract

We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. The mean-square rate of convergence of Euler approximations of solution to this equation is obtained.