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

• Autores: Dawei Hong, Shushuang Man, Jean-Camille Birget, Desmond S. Lun
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 51, Nº. 1, 2014, págs. 1-18
• Idioma: inglés
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• Resumen

  • 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