Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with $$ 1/4<H <1/2$$.

Abstract

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $$ H \in \left( 1/4, 1/2 \right) $$ . Toward 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.