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arXiv · 1111.6331

A wavelet-based approximation of fractional Brownian motion with a parallel algorithm

Dawei Hong·Shushuang Man·Jean-Camille Birget·Desmond Lun
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Abstract

We construct a wavelet-based almost sure uniform approximation of fractional Brownian motion (fBm) B_t^(H), t in [0, 1], of Hurst index H in (0, 1). Our results show that by Haar wavelets which merely have one vanishing moment, an almost sure uniform expansion of fBm of H in (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an fBm efficiently.

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Dawei Hong, Shushuang Man, Jean-Camille Birget, Desmond Lun. 2011-11-28. A wavelet-based approximation of fractional Brownian motion with a parallel algorithm. https://arxiv.org/abs/1111.6331

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