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A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

Part of: Numerical methods in Fourier analysis Stochastic processes Computer aspects of numerical algorithms

Published online by Cambridge University Press:  30 January 2018

Dawei Hong ,
Shushuang Man ,
Jean-Camille Birget  and
Desmond S. Lun
Dawei Hong*
Affiliation:
Rutgers University
Shushuang Man*
Affiliation:
Southwest Minnesota State University
Jean-Camille Birget*
Affiliation:
Rutgers University
Desmond S. Lun*
Affiliation:
Rutgers University
*
∗ Postal address: Center for Computational and Integrative Biology, Department of Computer Science, Rutgers University, Camden, NJ 08102, USA.
∗∗∗ Postal address: Department of Mathematics and Computer Science, Southwest Minnesota State University, Marshall, MN 56258, USA.
∗ Postal address: Center for Computational and Integrative Biology, Department of Computer Science, Rutgers University, Camden, NJ 08102, USA.
∗ Postal address: Center for Computational and Integrative Biology, Department of Computer Science, Rutgers University, Camden, NJ 08102, USA.
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Abstract

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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.

Keywords

Fractional Brownian motionwavelet expansion of stochastic integralalmost-sure uniform approximation

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 65T60: Wavelets 65Y05: Parallel computation
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 1 - 18
Copyright
© Applied Probability Trust 

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