A simple construction of the fractional Brownian motion

In this work we introduce correlated random walks on Z. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is the fractional Brownian motion. We have to use two radically different models for both cases 1/2 less than or equal to H < 1 and 0 < H < 1/2. (C) 2003 Elsevier B.V. All rights reserved.