Simulation and Analysis of a Power Law Fluctuation Generator

  • H. Fanchiotti
  • C. A. García Canal
  • N. Martínez
Conference paper


Recently, Sato, Takayasu and Sawada (2000) constructed an analog circuit able to generate a signal corresponding to a time series with fluctuations having a probability density function with a power law tail. The exponent of the power law can be arbitrarily fixed by tuning an appropriate resistance. In a sense it is the analog of a differential equation of the Langevin type including both multiplicative and additive noise. The authors claim that their circuit could be used in the near future as a simulator-generator of financial market fluctuations and consequently as a tool for risk estimations and forecasts.

After a discussion on the stability conditions for multiplicative noise, we present an analysis of the power law fluctuation generator in connection with the electronic components and their corresponding parameters. A circuit simulation completes our study.


Probability Density Function Operational Amplifier Multiplicative Noise Bode Plot Bide Plot 
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    Sato A. Takayasu H, Sawada Y (2000) Power law fluctuation generator based on analog electrical circuit. Fractals 8:219–225Google Scholar
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    Schenzle A, Brand H (1979) Multiplicative stochastic processes in statistical physics Physical Review A20:1628Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • H. Fanchiotti
    • 1
  • C. A. García Canal
    • 1
  • N. Martínez
    • 2
  1. 1.Laboratorio de Física Teórica, Departamento de FisicaUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.Departamento de FísicaUniversidad Nacional de La PlataLa PlataArgentina

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