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Universal behaviors of the multi-time correlation functions of random processes with renewal: The step noise case (the random velocity of a Lévy walk)

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  • Bianucci, Marco
  • Bologna, Mauro
  • Lagomarsino-Oneto, Daniele
  • Mannella, Riccardo

Abstract

Stochastic processes with renewal properties, also known as semi-Markovian processes, are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable’s value jumps according to a prescribed Probability Density Function (PDF), p(ξ), after random waiting times θ. This model is relevant across many fields, including classical chaos, nonlinear hydrodynamics, quantum dots, cold atom dynamics, biological motion, foraging, and finance.

Suggested Citation

  • Bianucci, Marco & Bologna, Mauro & Lagomarsino-Oneto, Daniele & Mannella, Riccardo, 2026. "Universal behaviors of the multi-time correlation functions of random processes with renewal: The step noise case (the random velocity of a Lévy walk)," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015498
    DOI: 10.1016/j.chaos.2025.117536
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    References listed on IDEAS

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    1. Bianucci, Marco & Bologna, Mauro & Lagomarsino-Oneto, Daniele & Mannella, Riccardo, 2025. "Universal behavior of the two-times correlation functions of random processes with renewal," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    2. 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).
    3. Bianucci, Marco, 2022. "The correlated dichotomous noise as an exact M-Gaussian stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Bianucci, Marco, 2021. "Operators central limit theorem," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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