Fractional Brownian motion as a nonstationary process: An alternative paradigm for DNA sequences


Article discussing the fractional Brownian motion (FBM) as a nonstationary process and an alternative paradigm for DNA sequences.

Creation Date: April 1998
UNT College of Arts and Sciences
UNT Scholarly Works
Total Uses: 207
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Creator (Author):
Allegrini, Paolo

University of North Texas

Creator (Author):
Buiatti, Marco, 1972-

Università di Pisa

Creator (Author):
Grigolini, Paolo

University of North Texas; Università di Pisa; Istituto di Biofisica

Creator (Author):
West, Bruce J.

University of North Texas

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
  • Creation: April 1998

Article discussing the fractional Brownian motion (FBM) as a nonstationary process and an alternative paradigm for DNA sequences.

Department: Physics

Copyright 1998 American Physical Society. The following article appeared in Physical Review E, 57:4, pp. 4558-4567;


Abstract: The long-range correlations in DNA sequences are currently interpreted as an example of stationary fractional Brownian motion (FBM). First the authors show that the dynamics of a dichotomous stationary process with long-range correlations such as that used to model DNA sequences should correspond to Lévy statistics and not to FBM. To explain why, in spite of this, the statistical analysis of the data seems to be compatible with FBM, the authors notice that an initial Gaussian condition, generated by a process foreign to the mechanism establishing the long-range correlations and consequently implying a departure from the stationary condition is maintained approximately unchanged for very long times. This is so because due to the nature itself of the long-range correlation process, it takes virtually an infinite time for the system to reach the genuine stationary state. Then the authors discuss a possible generator of initial Gaussian conditions, based on a folding mechanism of the nucleic acid in the cell nucleus. The model adopted is compatible with the known biological and physical constraints, namely, it is shown to be consistent with the information of current biological literature on folding as well as with the statistical analyses of DNA sequences.

Physical Description:

10 p.

Keyword(s): DNA sequences | Fractional Brownian Motion
Source: Physical Review E, 1998, College Park: American Physical Society, pp. 4558-4567
UNT College of Arts and Sciences
UNT Scholarly Works
  • DOI: 10.1103/PhysRevE.57.4558 |
  • ARK: ark:/67531/metadc75416
Resource Type: Article
Format: Text
Access: Public
Publication Title: Physical Review E
Volume: 57
Issue: 4
Page Start: 4558
Page End: 4567
Pages: 10
Peer Reviewed: Yes