Permutation entropy of fractional Brownian motion and fractional Gaussian noise
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...
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2008
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| LEADER | 10182caa a22008417a 4500 | ||
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| 001 | PAPER-5866 | ||
| 003 | AR-BaUEN | ||
| 005 | 20250821090813.0 | ||
| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-49649105312 | |
| 030 | |a PYLAA | ||
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Zunino, L. | |
| 245 | 1 | 0 | |a Permutation entropy of fractional Brownian motion and fractional Gaussian noise |
| 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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| 504 | |a Rosso, O.A., Zunino, L., Pérez, D.G., Figliola, A., Larrondo, H.A., Garavaglia, M., Martín, M.T., Plastino, A., (2007) Phys. Rev. E, 76, p. 061114 | ||
| 504 | |a Zunino, L., Pérez, D.G., Martín, M.T., Plastino, A., Garavaglia, M., Rosso, O.A., (2007) Phys. Rev. E, 75, p. 021115 | ||
| 504 | |a Bandt, C., Shiha, F., (2007) J. Time Ser. Anal., 28, p. 646 | ||
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| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a 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. © 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: 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. O.A.R. gratefully acknowledges support from Australian Research Council (ARC) Centre of Excellence in Bioinformatics, Australia. Appendix A For a Gaussian process with stationary increments and embedding dimension D = 3 , Bandt and Shiha (see Ref. [20] , pp. 656–659) found that p ( π 123 ) = p ( π 321 ) = u / 2 and p ( π 132 ) = p ( π 213 ) = p ( π 231 ) = p ( π 312 ) = ( 1 − u ) / 4 . In the case of a stationary Gaussian process with covariance ρ ( τ ) they shown that p ( π 123 ) is given by (A.1) p ( π 123 ) ( τ ) = 1 π arcsin ( 1 π 1 − ρ ( 2 τ ) 1 − ρ ( τ ) ) . Thus, for fractional Gaussian noise we should replace Eq. (8) in the last expression. 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 and Shiha shown that (A.2) p ( π 123 ) ( τ ) = 1 π arcsin ( 2 H − 1 ) for all τ , with H the Hurst parameter. For embedding dimension D = 4 they also found the relative frequencies for these processes. For a stationary Gaussian process and arbitrary τ > 0 , (A.3) 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 ) , 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 (A.4) 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 ) ] , 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 ) ] . For fractional Brownian motion, Bandt and Shiha obtained the same formula but with (A.5) 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 , α 7 = 3 2 H − 2 2 H − 1 2 H + 1 , α 8 = 2 2 H − 1 3 H . | ||
| 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), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 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 FRACTIONAL BROWNIAN MOTION |
| 690 | 1 | 0 | |a FRACTIONAL GAUSSIAN NOISE |
| 690 | 1 | 0 | |a PERMUTATION ENTROPY |
| 700 | 1 | |a Pérez, D.G. | |
| 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. 372 |h pp. 4768-4774 |k n. 27-28 |p Phys Lett Sect A Gen At Solid State Phys |x 03759601 |w (AR-BaUEN)CENRE-348 |t Physics Letters, Section A: General, Atomic and Solid State Physics | |
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