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A causal multifractal stochastic equation and its statistical properties


  • F. Schmitt



Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to discrete cascades. Here a causal log-normal stochastic process is introduced; its multifractal properties are demonstrated together with other properties such as the composition rule for scale dependence and stochastic differential equations for time and scale evolutions. This multifractal stochastic process is continuous in scale ratio and in time. It has a simple generating equation and can be used to generate sequentially time series of any length. Copyright Springer-Verlag Berlin/Heidelberg 2003

Suggested Citation

  • F. Schmitt, 2003. "A causal multifractal stochastic equation and its statistical properties," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 34(1), pages 85-98, July.
  • Handle: RePEc:spr:eurphb:v:34:y:2003:i:1:p:85-98
    DOI: 10.1140/epjb/e2003-00199-x

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    References listed on IDEAS

    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, June.
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    Cited by:

    1. Calif, Rudy & Schmitt, Fran├žois G. & Huang, Yongxiang, 2013. "Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4106-4120.

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