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An accurate fractional Brownian motion generator

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  • Rambaldi, Sandro
  • Pinazza, Ombretta

Abstract

A new algorithm for the simulation of fractional Brownian motion is suggested. This algorithm has been tested and compared with previous ones. Clear improvements in the statistical and scaling properties of the process, built with our algorithm, are shown. Large improvements have been achieved for short times and for Hurst's exponents less then 0.5, i.e. for path with high fractal dimension. A new strategy to generate fractional Brownian motions, based on the use of moments of increasing size blocks, is then described. This numerical method proved to be fast and accurate.

Suggested Citation

  • Rambaldi, Sandro & Pinazza, Ombretta, 1994. "An accurate fractional Brownian motion generator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(1), pages 21-30.
    • Handle: RePEc:eee:phsmap:v:208:y:1994:i:1:p:21-30
    DOI: 10.1016/0378-4371(94)90531-2
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    References listed on IDEAS

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    1. Wallis, Kenneth F, 1969. "Some Recent Developments in Applied Econometrics: Dynamic Models and Simultaneous Equation Systems," Journal of Economic Literature, American Economic Association, vol. 7(3), pages 771-796, September.
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    Cited by:

    1. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.
    2. Steven B. Lowen, 1999. "Efficent Generation of Fractional Brownian Motion for Simulation of Infrared Focal-plane Array Calibration Drift," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 445-456, December.

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