Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### A simple construction of the fractional Brownian motion

Auteur(s):

Code(s) de Classification MSC:

• 60F17 Functional limit theorems; invariance principles
• 60G15 Gaussian processes
• 60G17 Sample path properties
• 60K99 None of the above but in this section

Résumé: 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 ${1\over2}\leq H<1$ and $0< H<{1\over2}$ . This result provides an algorithm for the simulation of the fractional Brownian motion, which appears to be quite efficient.

Mots Clés: Correlated random walks ; random environment ; Fractional Brownian motion

Date: 2002-10-23

Prépublication numéro: PMA-765

Postscript file : PMA-765.ps

Pdf file : PMA-765.pdf