Date: April 27, 2006
Creator: Allegrini, Paolo; Barbi, Francesco; Grigolini, Paolo & Paradisi, Paolo
Description: In this article, the authors consider two different approaches, to which the authors refer to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times. The authors show that different time series with the same waiting time distribution are not necessarily statistically equivalent, and might generate different physical properties. Renewal generates aging and anomalous scaling, while modulation yields no significant aging and either ordinary or anomalous diffusion, according to the dynamic prescription adopted. The authors show, in fact, that the physical realization of modulation generates two classes of events. The events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time, and consequently are numerous; the events of the second class are identified with the abrupt changes from one to another exponential prescription, and consequently are rare. The events of the second class, although rare, determine the scaling of the diffusion process, and for this reason the authors term them as crucial events. According to the prescription adopted to produce modulation, the distribution density of the time distances between two consecutive crucial events might have, or not, a diverging second moment. In the ...
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