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Spurious memory in non-equilibrium stochastic models of imitative behavior

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  • Vygintas Gontis
  • Aleksejus Kononovicius

Abstract

The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent $3/2$ of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.

Suggested Citation

  • Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    • Handle: RePEc:arx:papers:1707.09801
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    References listed on IDEAS

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    Cited by:

    1. Kononovicius, Aleksejus, 2021. "Supportive interactions in the noisy voter model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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.
    3. Vygintas Gontis & Aleksejus Kononovicius, 2019. "Bessel-like birth-death process," Papers 1904.13064, arXiv.org, revised Oct 2019.
    4. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    5. Vygintas Gontis & Aleksejus Kononovicius, 2017. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Papers 1712.05121, arXiv.org, revised Feb 2018.
    6. Gontis, V. & Kononovicius, A., 2020. "Bessel-like birth–death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.
    8. Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    9. Gontis, V. & Kononovicius, A., 2018. "The consentaneous model of the financial markets exhibiting spurious nature of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1075-1083.
    10. Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.

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