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

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