Discretization error of reflected fractional Brownian motion

Abstract

The long-range dependence and self-similarity of fractional Brownian motion make it an attractive model for traffic in many data transfer networks. Reflected fractional Brownian Motion appears in the storage process of such a network. In this paper, we focus on the simulation of reflected fractional Brownian motion using a straightforward discretization scheme and we show that its strong error is of order hH, where h is the discretization step and H ∈ (0,1) is the Hurst index.