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An analytical approach for describing self-similar random processes with positive variables

Author

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  • Koverda, V.P.
  • Skokov, V.N.

Abstract

An analytical approach to describe self-similar random processes with positive variables is proposed. The approach is based on the use of a system of nonlinear stochastic equations describing stochastic dynamics at coupled interacting nonequilibrium phase transitions. The solutions of the proposed equations are random processes with power-law behavior of spectral densities and probability density functions. An entropy analysis of stability of random processes is carried out.

Suggested Citation

  • Koverda, V.P. & Skokov, V.N., 2025. "An analytical approach for describing self-similar random processes with positive variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 673(C).
    • Handle: RePEc:eee:phsmap:v:673:y:2025:i:c:s037843712500336x
    DOI: 10.1016/j.physa.2025.130684
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    References listed on IDEAS

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    1. Corral, Álvaro, 2015. "Scaling in the timing of extreme events," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 99-112.
    2. Koverda, V.P. & Skokov, V.N., 2012. "Maximum entropy in a nonlinear system with a 1/f power spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 21-28.
    3. Koverda, V.P. & Skokov, V.N., 2005. "The origin of 1/f fluctuations and scale transformations of time series at nonequilibrium phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 203-216.
    4. 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).
    5. Koverda, V.P. & Skokov, V.N., 2023. "Governing stochastic equation for a self-similar random process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    6. Skokov, V.N. & Koverda, V.P. & Reshetnikov, A.V. & Vinogradov, A.V., 2006. "1/f fluctuations under acoustic cavitation of liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 63-69.
    7. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
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