Simulation and Analysis of a Power Law Fluctuation Generator
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.
KeywordsProbability Density Function Operational Amplifier Multiplicative Noise Bode Plot Bide Plot
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