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Non-Poisson dichotomous noise: higher-order correlation functions and aging

P. Allegrini·P. Grigolini·L. Palatella·B. J. West
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Abstract

We study a two-state symmetric noise, with a given waiting time distribution $ψ(τ)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $ψ(τ)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.

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P. Allegrini, P. Grigolini, L. Palatella, B. J. West. 2004-02-19. Non-Poisson dichotomous noise: higher-order correlation functions and aging. https://doi.org/10.1103/physreve.70.046118

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