A simple construction of the Fractional Brownian motion

Details A simple construction of the Fractional Brownian motion A simple construction of the Fractional Brownian motion

2002-10-17

arxiv.org/abs/math/0210272v1

Mathematics

Probability

15 pages, 3 figures

Scientific paper

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

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