Modeling Gaussian and non-Gaussian 1/f noise by the linear stochastic differential equations

The ubiquitously observable 1/f noise is mostly Gaussian but sometimes the non-Gaussianity is recognizable, as well. Here we consider stochastic models of 1/f noise based on the linear stochastic differential equations with the very slowly varying coefficients (intensity of the white noise and relaxation rate) or consisting of a superposition of uncorrelated components with different distributions of these coefficients. We explore the conditions in which the modeled signal exhibiting 1/f^β noise is Gaussian and when it is non-Gaussian, i.e., the power-law distributed.