Statistics of extreme low-frequency fluctuations in a stationary stochastic process exhibiting the 1/f spectrum

A study was conducted to show the properties of extreme low-frequency fluctuations in a stationary stochastic process, with an intensity spectrum, inversely proportional to the frequency (1/f). The I/f processes were projected by the scale-invariant fluctuation distribution. The scale invariance of the random process was associated with the critical behavior and the self-organization of complex system. The fluctuation-power spectrum in the self-organized criticality models was found to be inversely proportional to the frequency squared. Random processes, containing the 1/f power spectrum were obtained in a set of two differential nonlinear stochastic equations, which defined the interaction of heterogeneous phase transition. The simulation of the white noise was realized by the sequence of Gaussian random numbers of zero mean value. Results show that durations of low-frequency fluctuations exhibit power dependence.