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Resemblance of the power-law scaling behavior of a non-Markovian and nonlinear point processes

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  • Kononovicius, Aleksejus
  • Kazakevičius, Rytis
  • Kaulakys, Bronislovas

Abstract

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non-Markovian point process exhibit power-law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a possible link between nonlinearity and apparent non-Markovian behavior.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007111
    DOI: 10.1016/j.chaos.2022.112508
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