Simulation and Analysis of a Power Law Fluctuation Generator

Abstract

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.