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A general framework for simulation of fractional fields

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  • Cohen, Serge
  • Lacaux, Céline
  • Ledoux, Michel

Abstract

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields, including linear and harmonizable fractional stable fields. Almost sure and Lr-norm rates of convergence, relying on asymptotic developments of the deterministic kernels, are presented as a consequence of an approximation result concerning series of symmetric random variables. When the control measure is infinite, normal approximation has to be used as a complement. The general framework is illustrated by simulations of classical fractional fields.

Suggested Citation

  • Cohen, Serge & Lacaux, Céline & Ledoux, Michel, 2008. "A general framework for simulation of fractional fields," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1489-1517, September.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:9:p:1489-1517
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    References listed on IDEAS

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    1. Serge Cohen & Murad S. Taqqu, 2004. "Small and Large Scale Behavior of the Poissonized Telecom Process," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 363-379, December.
    2. Stoev, Stilian A. & Taqqu, Murad S., 2006. "How rich is the class of multifractional Brownian motions?," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 200-221, February.
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    Cited by:

    1. Heinrich, Claudio & Pakkanen, Mikko S. & Veraart, Almut E.D., 2019. "Hybrid simulation scheme for volatility modulated moving average fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 224-244.

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