Approximation of stochastic differential equations driven by step fractional Brownian motion

Abstract. The aim of this paper is to approximate the solution of a stochastic differential equation driven by step fractional Brownian motion using a series expansion for the noise. We prove that the solution of the approximating equations converges in probability to the solution of the given equation. We illustrate the approximation through the model for the price of risky assets from mathematical finance. The figures are generated in GeoGebra.