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A simple construction of the Fractional Brownian motion

Enriquez Nathanael
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Abstract

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.

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Enriquez Nathanael. 2002-10-17. A simple construction of the Fractional Brownian motion. https://arxiv.org/abs/math/0210272

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