Power law fluctuation generator based on analog electrical circuit

We constructed an analog circuit generating fluctuations of which a probabi lity density function has power law tails. In the circuit, fluctuations wit h an arbitrary exponent of the power law can be obtained by tuning the resi stance. A theory of a differential equation with both multiplicative and ad ditive noises which describes the circuit is introduced. The circuit is com posed of a noise generator, an analog multiplier and an integration circuit . Sequential outputs of the circuit are observed and their probability dens ity function and autocorrelation coefficients are shown. It is found that c orrelation time of the autocorrelation coefficient is dependent on the powe r law exponent.