Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**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