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Nonlinear stochastic models of 1/f noise and power-law distributions

Author

Listed:
  • Kaulakys, Bronislovas
  • Ruseckas, Julius
  • Gontis, Vygintas
  • Alaburda, Miglius

Abstract

Starting from the developed generalized point process model of 1/f noise [B. Kaulakys et al., Phys. Rev. E 71 (2005) 051105] we derive the nonlinear stochastic differential equations for the signal exhibiting 1/fβ noise and 1/xλ distribution density of the signal intensity with different values of β and λ. The processes with 1/fβ are demonstrated by the numerical solution of the derived equations with the appropriate restriction of the diffusion of the signal in some finite interval. The proposed consideration may be used for modeling and analysis of stochastic processes in different systems with the power-law distributions, long-range memory or with the elements of self-organization.

Suggested Citation

  • Kaulakys, Bronislovas & Ruseckas, Julius & Gontis, Vygintas & Alaburda, Miglius, 2006. "Nonlinear stochastic models of 1/f noise and power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 217-221.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:217-221
    DOI: 10.1016/j.physa.2006.01.017
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    Citations

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    Cited by:

    1. Kononovicius, A. & Ruseckas, J., 2015. "Nonlinear GARCH model and 1/f noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 74-81.
    2. Aleksejus Kononovicius & Vygintas Gontis, 2012. "Three-state herding model of the financial markets," Papers 1210.1838, arXiv.org, revised Jan 2013.
    3. Aleksejus Kononovicius & Vygintas Gontis & Valentas Daniunas, 2012. "Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance," Papers 1202.3533, arXiv.org, revised Jun 2012.
    4. Kononovicius, Aleksejus & Kazakevičius, Rytis & Kaulakys, Bronislovas, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Vygintas Gontis & Aleksejus Kononovicius & Stefan Reimann, 2012. "The class of nonlinear stochastic models as a background for the bursty behavior in financial markets," Papers 1201.3083, arXiv.org, revised May 2012.
    6. Aleksejus Kononovicius & Rytis Kazakeviv{c}ius & Bronislovas Kaulakys, 2022. "Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes," Papers 2205.07563, arXiv.org, revised Jul 2022.
    7. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    8. Aleksejus Kononovicius & Bronislovas Kaulakys, 2022. "$1/f$ noise from the sequence of nonoverlapping rectangular pulses," Papers 2210.11792, arXiv.org, revised Mar 2023.
    9. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.

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