Power - Law Shot

We explore the behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1=f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1=f shot noise for in the range 0 < < 2. For other parameters the amplitude probability density function is a L evy-stable random variable with dimension less than unity. This process then behaves as a fractal shot noise that does not converge to a Gaussian amplitude distribution as the driving rate increases without limit. Fractal shot noise is a stationary continuous-time process that is fundamentally di erent from fractional Brownian motion. We consider several physical processes that are well described by power-law shot noise in certain domains: 1=f shot noise, Cherenkov radiation from a random stream of charged particles, di usion of randomly injected concentration packets, the electric eld at the growing edge of a quantum wire, and the mass distribution of solid-particle aggregates.