Some stochastic processes yielding a f−ν type of spectral density

Abstract

Using a specific definition of spectral density for nonstationary stochastic processes, a randomization procedure is used to analyze three types of process likely to be important in physical applications. Thus the symmetric random walk, Ornstein‐Uhlenbeck, and shot‐noise models are generalized and are shown to lead to spectral densities of the form f^−ν at low frequencies. Since most systems of interest will contain many contributing sources to the fluctuation, limit probability distributions are employed. It appears that randomized shot noise is probably the relevant process in the behavior of semiconductor current noise.