Fractional Brownian motion approximation based on fractional integration of a white noise

We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of Tractional in tegration/differentiation of a white Gaussian noise. We consider correlatio n properties of the approximation to fractional Gaussian noise and point to the peculiarities of persistent and anti-persistent behaviors. We also inv estigate self-similarity properties of the approximation to fractional Brow nian motion, namely, 'tau (H) laws' for the structure function and the rang e. We conclude that the models proposed serve as a convenient tool for mode lling of natural processes and testing and improvement of methods aimed at analysis and interpretation of experimental data. (C) 2000 Elsevier Science Ltd. All rights reserved.