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

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

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

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.

Keywords: Renewal processes; CTRW; Lévy walk; Universal multi times correlation function (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015498

DOI: 10.1016/j.chaos.2025.117536

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