# Numerical scheme for stochastic differential equations driven by fractional Brownian motion with 1/4 < H < 1/2

## TL;DR

This paper develops a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter between 1/4 and 1/2, achieving a convergence rate of n^(2H+rho).

## Contribution

It introduces a novel numerical approximation method using Doss-Sussmann representation and Taylor expansion for fractional Brownian motion with H in (1/4, 1/2).

## Key findings

- Convergence rate of n^(2H+rho) for the scheme.
- Application of Doss-Sussmann representation in numerical approximation.
- Effective handling of fractional Brownian motion with H in (1/4, 1/2).

## Abstract

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an approximation of this representation using a first order Taylor expansion. The obtained rate of convergence is n^(2H+rho), for rho small enough.