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

Author

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  • Koverda, V.P.
  • Skokov, V.N.

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.

Suggested Citation

  • Koverda, V.P. & Skokov, V.N., 2020. "Establishment of a stationary stochastic process with a 1/f spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120302788
    DOI: 10.1016/j.physa.2020.124581
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