Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy
In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability distribu...
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2008
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| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-49649083517 | |
| 030 | |a PHYAD | ||
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Zunino, L. | |
| 245 | 1 | 0 | |a Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy |
| 260 | |c 2008 | ||
| 270 | 1 | 0 | |m Zunino, L.; Centro de Investigaciones Ópticas, C.C. 124 Correo Central, 1900 La Plata, Argentina; email: lucianoz@ciop.unlp.edu.ar |
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| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability distribution, is shown to be a powerful tool to characterize fractal stochastic processes. It allows for a better discrimination of the processes than the Shannon counterpart for appropriate ranges of values of the entropic index. Moreover, we find the optimum value of this entropic index for the stochastic processes under study. © 2008 Elsevier B.V. All rights reserved. |l eng | |
| 536 | |a Detalles de la financiación: Fondo Nacional de Desarrollo Científico, Tecnológico y de Innovación Tecnológica, 11060512 | ||
| 536 | |a Detalles de la financiación: Australian Research Council | ||
| 536 | |a Detalles de la financiación: Office for the Advancement of Research, John Jay College of Criminal Justice | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, 5687/05, 6036/05, PIP 0029/98 | ||
| 536 | |a Detalles de la financiación: Comisión Nacional de Investigación Científica y Tecnológica, CONICYT | ||
| 536 | |a Detalles de la financiación: Pontificia Universidad Católica de Valparaíso, 123.788/2007 | ||
| 536 | |a Detalles de la financiación: 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. OAR gratefully acknowledges support from Australian Research Council (ARC) Centre of Excellence in Bioinformatics, Australia. Appendix Bandt and Shiha (see Ref. [37, pp. 656–659] ) have recently found the relative frequencies for a stationary Gaussian process, embedding dimension D = 4 and arbitrary τ > 0 , p ( π 1234 ) ( τ ) = p ( π 4321 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 1 + 2 arcsin α 2 ) , p ( π 3142 ) ( τ ) = p ( π 2413 ) ( τ ) = 1 8 + 1 4 π ( 2 arcsin α 3 + arcsin α 4 ) , p ( π 4231 ) ( τ ) = p ( π 1324 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 4 − 2 arcsin α 5 ) , p ( π 2143 ) ( τ ) = p ( π 3412 ) ( τ ) = 1 8 + 1 4 π ( 2 arcsin α 6 + arcsin α 1 ) , p ( π 1243 ) ( τ ) = p ( π 2134 ) ( τ ) = p ( π 3421 ) ( τ ) = p ( π 4312 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 7 − arcsin α 1 − arcsin α 5 ) , p ( π 1423 ) ( τ ) = p ( π 4132 ) ( τ ) = p ( π 3241 ) ( τ ) = p ( π 2314 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 7 − arcsin α 4 − arcsin α 5 ) , p ( π 3124 ) ( τ ) = p ( π 1342 ) ( τ ) = p ( π 4213 ) ( τ ) = p ( π 2431 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 3 + arcsin α 8 − arcsin α 5 ) , (12) p ( π 1432 ) ( τ ) = p ( π 4123 ) ( τ ) = p ( π 2341 ) ( τ ) = p ( π 3214 ) ( τ ) = 1 8 + 1 4 π ( arcsin α 6 − arcsin α 8 + arcsin α 2 ) , where α 1 = 2 ρ ( 2 τ ) − ρ ( τ ) − ρ ( 3 τ ) 2 [ 1 − ρ ( τ ) ] , α 2 = 2 ρ ( τ ) − ρ ( 2 τ ) − 1 2 [ 1 − ρ ( τ ) ] , α 3 = ρ ( 2 τ ) + ρ ( 3 τ ) − ρ ( τ ) − 1 2 [ 1 − ρ ( 2 τ ) ] [ 1 − ρ ( 3 τ ) ] , α 4 = ρ ( τ ) − ρ ( 3 τ ) 2 [ 1 − ρ ( 2 τ ) ] , α 5 = 1 2 1 − ρ ( 2 τ ) 1 − ρ ( τ ) , α 6 = ρ ( τ ) + ρ ( 3 τ ) − ρ ( 2 τ ) − 1 2 [ 1 − ρ ( τ ) ] [ 1 − ρ ( 3 τ ) ] , (13) α 7 = ρ ( τ ) + ρ ( 2 τ ) − ρ ( 3 τ ) − 1 2 [ 1 − ρ ( τ ) ] [ 1 − ρ ( 2 τ ) ] , α 8 = ρ ( τ ) − ρ ( 2 τ ) [ 1 − ρ ( τ ) ] [ 1 − ρ ( 3 τ ) ] . Thus, for fractional Gaussian noise we should replace Eq. (10) in the last expressions. Since the fractional Brownian motion is a self-similar process, the relative frequencies p ( π i ) do not depend on the value of τ . Moreover, Bandt & Shiha have also obtained the same formulae Eq. (12) for fBm and embedding dimension D = 4 but with α 1 = 1 + 3 2 H − 2 2 H + 1 2 , α 2 = 2 2 H − 1 − 1 , α 3 = 1 − 3 2 H − 2 2 H 2 ⋅ 6 H , α 4 = 3 2 H − 1 2 2 H + 1 , α 5 = 2 H − 1 , α 6 = 2 2 H − 3 2 H − 1 2 ⋅ 3 H , (14) α 7 = 3 2 H − 2 2 H − 1 2 H + 1 , α 8 = 2 2 H − 1 3 H , where H is the Hurst parameter. | ||
| 593 | |a Centro de Investigaciones Ópticas, C.C. 124 Correo Central, 1900 La Plata, Argentina | ||
| 593 | |a Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina | ||
| 593 | |a Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Argentina | ||
| 593 | |a Instituto de Física, Pontificia Universidad Católica de Valparaíso (PUCV), 23-40025 Valparaíso, Chile | ||
| 593 | |a Instituto de Física (IFLP-CCT), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina | ||
| 593 | |a Buenos Aires Scientific Research Commission (CIC), C.C. 727, 1900 La Plata, Argentina | ||
| 593 | |a Argentina's National Council (CCT-CONICET), C.C. 727, 1900 La Plata, Argentina | ||
| 593 | |a Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, University Drive, Callaghan, NSW 2308, Australia | ||
| 593 | |a Chaos and Biology Group, Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a BANDT & POMPE METHOD |
| 690 | 1 | 0 | |a FRACTIONAL BROWNIAN MOTION |
| 690 | 1 | 0 | |a FRACTIONAL GAUSSIAN NOISE |
| 690 | 1 | 0 | |a TSALLIS ENTROPY |
| 690 | 1 | 0 | |a BROWNIAN MOVEMENT |
| 690 | 1 | 0 | |a GAUSSIAN NOISE (ELECTRONIC) |
| 690 | 1 | 0 | |a RISK ASSESSMENT |
| 690 | 1 | 0 | |a STOCHASTIC PROGRAMMING |
| 690 | 1 | 0 | |a TRELLIS CODES |
| 690 | 1 | 0 | |a ENTROPIC INDEXES |
| 690 | 1 | 0 | |a FRACTIONAL BROWNIAN MOTION |
| 690 | 1 | 0 | |a FRACTIONAL GAUSSIAN NOISE |
| 690 | 1 | 0 | |a OPTIMUM VALUE |
| 690 | 1 | 0 | |a PERMUTATION ENTROPY |
| 690 | 1 | 0 | |a POW ERFUL TOOL |
| 690 | 1 | 0 | |a RANGES OF VALUES |
| 690 | 1 | 0 | |a STOCHASTIC PROCESSING |
| 690 | 1 | 0 | |a TSALLIS ENTROPY |
| 690 | 1 | 0 | |a PROBABILITY DISTRIBUTIONS |
| 700 | 1 | |a Pérez, D.G. | |
| 700 | 1 | |a Kowalski, A. | |
| 700 | 1 | |a Martín, M.T. | |
| 700 | 1 | |a Garavaglia, Mario José | |
| 700 | 1 | |a Plastino, Angel Luis | |
| 700 | 1 | |a Rosso, O.A. | |
| 773 | 0 | |d 2008 |g v. 387 |h pp. 6057-6068 |k n. 24 |p Phys A Stat Mech Appl |x 03784371 |w (AR-BaUEN)CENRE-280 |t Physica A: Statistical Mechanics and its Applications | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.physa.2008.07.004 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03784371_v387_n24_p6057_Zunino |y Handle |
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