Simulation of Weakly Self-Similar Stationary Increment Sub’ð ð Þ-Processes: A Series Expansion Approach

Abstract. We consider simulation of Sub ’ð Þ-processes that are weakly selfsimilar with stationary increments in the sense that they have the covariance function Rt; ð sÞ 1 2 t2H þ s 2H jtsj 2H or some H 2 (0, 1). This means that the second order structure of the processes is that of the fractional Brownian motion. Also, if H> 1 2 then the process is long-range dependent. The simulation is based on a series expansion of the fractional Brownian motion due to Dzhaparidze and van Zanten. We prove an estimate of the accuracy of the simulation in the space C([0, 1]) of continuous functions equipped with the usual sup-norm. The result holds also for the fractional Brownian motion which may be considered as a special case of a Subx2 =2ð Þ-process