Allegrini P, Grigolini P, Palatella L, West BJ. Non-Poisson dichotomous noise: higher-order correlation functions and aging.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004;
70:046118. [PMID:
15600471 DOI:
10.1103/physreve.70.046118]
[Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2004] [Indexed: 05/24/2023]
Abstract
We study a two-state symmetric noise, with a given waiting time distribution psi (tau) , and focus our attention on the connection between the four-time and two-time correlation functions. The transition of psi (tau) from the exponential to the nonexponential 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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