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March 2014 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
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J. Appl. Probab. 51(1): 1-18 (March 2014). DOI: 10.1239/jap/1395771410

Abstract

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.

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Dawei Hong. Shushuang Man. Jean-Camille Birget. Desmond S. Lun. "A wavelet-based almost-sure uniform approximation of fractional Brownian motion with a parallel algorithm." J. Appl. Probab. 51 (1) 1 - 18, March 2014. https://doi.org/10.1239/jap/1395771410

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1294.60065
MathSciNet: MR3189438
Digital Object Identifier: 10.1239/jap/1395771410

Subjects:
Primary: 60G22
Secondary: 65T60, 65Y05

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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