Stability of Random Processes with the 1/f ^α Spectrum

Extreme fluctuations have been modeled based on point nonpotential and potential systems of stochastic equations, in which white noise induces random processes with a power-law frequency dependence of the power spectra. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which indicates their stability. The stability of fluctuation processes with 1/f  ^α power spectra has been analyzed based on the principle of maximum information entropy.