Establishment of a stationary stochastic process with a 1/f spectrum

Abstract

The relaxation of random processes with a 1/f power spectrum has been studied. The stablest random processes on the classical maximum entropy principle have been found. The time of establishment of a stationary random process has been determined for a random process with a 1/f spectrum. A paradoxical result has been obtained: the longer the integration time step, and thus the rougher the approximation of white noise by a sequence of random numbers, the earlier comes a stationary process with a 1/f power spectrum. For a precise stochastic equation with white noise it is shown that the process tends to a nonstationary one.