Resumen de A wavelet-based almost-sure uniform approximation of fractional brownian motion with a parallel algorithm

Dawei Hong, Shushuang Man, Jean-Camille Birget, Desmond S. Lun

• We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))t?[0,1] of Hurst index H ? (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ? (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