Renewal, modulation, and superstatistics in times series (Articolo in rivista)

Type
Label
  • Renewal, modulation, and superstatistics in times series (Articolo in rivista) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1103/PhysRevE.73.046136 (literal)
Alternative label
  • Paolo Allegrini; Francesco Barbi; Paolo Grigolini; Paolo Paradisi (2006)
    Renewal, modulation, and superstatistics in times series
    in Physical review. E, Statistical, nonlinear and soft matter physics (Online)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Paolo Allegrini; Francesco Barbi; Paolo Grigolini; Paolo Paradisi (literal)
Pagina inizio
  • 046136-1 (literal)
Pagina fine
  • 046136-13 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://pre.aps.org/abstract/PRE/v73/i4/e046136 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 73 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 13 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 4 (literal)
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
  • Google Scholar (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto Nazionale di Fisica della Materia, unità di Como, Via Valleggio 11, 22100 Como, Italy Dipartimento di Fisica \"E.Fermi\"-Università di Pisa, Largo Pontecorvo, 3 56127 Pisa, Italy Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA Istituto dei Processi Chimico Fisici del CNR, Area della Ricerca di Pisa, Via G. Moruzzi, 56124, Pisa, Italy ISAC-CNR, Sezione di Lecce, Strada Provinciale Lecce-Monteroni km 1.2 I-73100 Lecce, Italy (literal)
Titolo
  • Renewal, modulation, and superstatistics in times series (literal)
Abstract
  • We consider two different approaches, to which we refer to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times. We 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. We 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 we 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 former case the resulting diffusion process, although going through a transition regime very extended in time, will eventually become anomalous. In conclusion, modulation rather than ruling out the action of renewal events, produces crucial events hidden by clouds of exponential events, thereby setting the challenge for their identification. (literal)
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