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Aging and renewal events in sporadically modulated systems

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  • Allegrini, P.
  • Barbi, F.
  • Grigolini, P.
  • Paradisi, P.

Abstract

We describe a form of modulation, namely a dishomogeneous Poisson process whose event rate changes sporadically and randomly in time with a chosen prescription, so as to share many statistical properties with a corresponding non-Poisson renewal process. Using our prescription the correlation function and the waiting time distribution between events are the same. If we study a continuous-time random walk, where the walker has only two possible velocities, randomly established at the times of the events, we show that the two processes also share the same second moment. However, the modulated diffusion process undergoes a dynamical transition between superstatistics and a Lévy walk process, sharing the scaling properties of the renewal process only asymptotically. The aging experiment – based on the evaluation of the waiting time for the next event, given a certain time distance between another previous event and the beginning of the observation – seems to be the key experiment to discriminate between the two processes.

Suggested Citation

  • Allegrini, P. & Barbi, F. & Grigolini, P. & Paradisi, P., 2007. "Aging and renewal events in sporadically modulated systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 11-18.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:1:p:11-18
    DOI: 10.1016/j.chaos.2007.01.045
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    Cited by:

    1. Allegrini, Paolo & Paradisi, Paolo & Menicucci, Danilo & Laurino, Marco & Bedini, Remo & Piarulli, Andrea & Gemignani, Angelo, 2013. "Sleep unconsciousness and breakdown of serial critical intermittency: New vistas on the global workspace," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 32-43.
    2. Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-26, May.
    3. Chichigina, Olga A. & Valenti, Davide, 2021. "Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Iliopoulos, A. & Chorozoglou, D. & Kourouklas, C. & Mangira, O. & Papadimitriou, E., 2020. "Memory and renewal aging of strong earthquakes in Hellenic seismicity," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Paradisi, Paolo & Allegrini, Paolo, 2015. "Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 451-462.

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