A wavelet-based approximation of fractional Brownian motion with a parallel algorithm
Probability
2013-07-04 v3
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.
Cite
@article{arxiv.1111.6331,
title = {A wavelet-based approximation of fractional Brownian motion with a parallel algorithm},
author = {Dawei Hong and Shushuang Man and Jean-Camille Birget and Desmond Lun},
journal= {arXiv preprint arXiv:1111.6331},
year = {2013}
}
Comments
20 pages. J. of Applied Probability, to appear in March 2014