Permutation entropy of fractional Brownian motion and fractional Gaussian noise

L. Zunino; D. G. Pérez; M. T. Martín; M. Garavaglia; A. Plastino; O. A. Rosso

doi:10.1016/j.physleta.2008.05.026

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

L. Zunino, D. G. Pérez, M. T. Martín, M. Garavaglia, A. Plastino, O. A. Rosso

INSTITUTE OF PHYSICS

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82 Scopus citations

Abstract

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.

Original language	English
Pages (from-to)	4768-4774
Number of pages	7
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	372
Issue number	27-28
DOIs	https://doi.org/10.1016/j.physleta.2008.05.026
State	Published - 30 Jun 2008

Keywords

Fractional Brownian motion
Fractional Gaussian noise
Permutation entropy

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10.1016/j.physleta.2008.05.026

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title = "Permutation entropy of fractional Brownian motion and fractional Gaussian noise",

abstract = "We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.",

keywords = "Fractional Brownian motion, Fractional Gaussian noise, Permutation entropy",

author = "L. Zunino and P{\'e}rez, {D. G.} and Mart{\'i}n, {M. T.} and M. Garavaglia and A. Plastino and Rosso, {O. A.}",

note = "Funding Information: This work was partially supported by Consejo Nacional de Investigaciones Cient{\'i}ficas y T{\'e}cnicas (CONICET) (PIP 0029/98; 5687/05 and 6036/05), Argentina, Comisi{\'o}n Nacional de Investigaci{\'o}n Cient{\'i}fica y Tecnol{\'o}gica (CONICYT) (FONDECYT project No. 11060512), Chile, and Pontificia Universidad Cat{\'o}lica de Valpara{\'i}so (PUCV) (Project No. 123.788/2007), Chile. O.A.R. gratefully acknowledges support from Australian Research Council (ARC) Centre of Excellence in Bioinformatics, Australia. ",

year = "2008",

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doi = "10.1016/j.physleta.2008.05.026",

language = "English",

volume = "372",

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TY - JOUR

T1 - Permutation entropy of fractional Brownian motion and fractional Gaussian noise

AU - Zunino, L.

AU - Pérez, D. G.

AU - Martín, M. T.

AU - Garavaglia, M.

AU - Plastino, A.

AU - Rosso, O. A.

N1 - Funding Information: This work was partially supported by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) (PIP 0029/98; 5687/05 and 6036/05), Argentina, Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) (FONDECYT project No. 11060512), Chile, and Pontificia Universidad Católica de Valparaíso (PUCV) (Project No. 123.788/2007), Chile. O.A.R. gratefully acknowledges support from Australian Research Council (ARC) Centre of Excellence in Bioinformatics, Australia.

PY - 2008/6/30

Y1 - 2008/6/30

N2 - We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.

AB - We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.

KW - Fractional Brownian motion

KW - Fractional Gaussian noise

KW - Permutation entropy

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DO - 10.1016/j.physleta.2008.05.026

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VL - 372

SP - 4768

EP - 4774

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 27-28

ER -

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

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