Renewal, Modulation, and Superstatistics in Times Series

Description:

Article discussing two different approaches, referred to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times.

Creator(s):
Creation Date: April 27, 2006
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
Total Uses: 63
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Creator (Author):
Allegrini, Paolo

Istituto Nazionale di Fisica della Materia; Universit√° di Pisa

Creator (Author):
Barbi, Francesco

Universit√° di Pisa

Creator (Author):
Grigolini, Paolo

Universit√° di Pisa; University of North Texas; Area della Ricerca di Pisa

Creator (Author):
Paradisi, Paolo

Sezione di Lecce

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: April 27, 2006
Description:

Article discussing two different approaches, referred to as renewal and modulation, to generate time series with a nonexponential distribution of waiting times.

Degree:
Department: Physics
Note:

Copyright 2006 American Physical Society. The following article appeared in Physical Review E, 73:4; http://pre.aps.org/abstract/PRE/v73/i4/e046136

Note:

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.

Physical Description:

13 p.

Language(s):
Subject(s):
Keyword(s): renewals | modulations | superstatistics
Source: Physical Review E, 2006, College Park: American Physical Society
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.73.046136 |
  • ARK: ark:/67531/metadc40400
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 73
Issue: 4
Pages: 13
Peer Reviewed: Yes