Permutation entropy of fractional Brownian motion and fractional Gaussian noise. (English) Zbl 1221.60051
Summary: 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 and F. Shiha, J. Time Ser. Anal. 28, No. 5, 646–665 (2007; Zbl 1150.62037)] 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.
MSC:
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H40 | White noise theory |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Citations:
Zbl 1150.62037Software:
longmemoReferences:
| [1] | Bandt, C.; Pompe, B., Phys. Rev. Lett., 88, 174102 (2002) |
| [2] | Keller, K.; Lauffer, H., Int. J. Bifur. Chaos, 13, 2657 (2003) · Zbl 1046.37054 |
| [3] | Cao, Y.; Tung, W.; Gao, J. B.; Protopopescu, V. A.; Hively, L. M., Phys. Rev. E, 70, 046217 (2004) |
| [4] | Larrondo, H. A.; González, C. M.; Martín, M. T.; Plastino, A.; Rosso, O. A., Physica A, 356, 133 (2005) |
| [5] | Larrondo, H. A.; Martín, M. T.; González, C. M.; Plastino, A.; Rosso, O. A., Phys. Lett. A, 352, 421 (2006) · Zbl 1187.65003 |
| [6] | Kowalski, A.; Martín, M. T.; Plastino, A.; Rosso, O. A., Physica D, 233, 21 (2007) · Zbl 1147.82340 |
| [7] | Rosso, O. A.; Larrondo, H. A.; Martín, M. T.; Plastino, A.; Fuentes, M. A., Phys. Rev. Lett., 99, 154102 (2007) |
| [8] | Rosso, O.; Vicente, R.; Mirasso, C., Phys. Lett. A, 372, 1018 (2007) |
| [9] | Mandelbrot, B. B., The Fractal Geometry of Nature (1982), W.H. Freeman: W.H. Freeman New York · Zbl 0504.28001 |
| [10] | Voss, R. F., Phys. Rev. Lett., 68, 3805 (1992) |
| [11] | Allegrini, P.; Buiatti, M.; Grigolini, P.; West, B. J., Phys. Rev. E, 57, 4558 (1998) |
| [12] | Su, Z.-Y.; Wu, T., Physica A, 380, 418 (2007) |
| [13] | Mandelbrot, B. B.; Ness, J. W.V., SIAM Rev., 4, 422 (1968) |
| [14] | Abry, P.; Flandrin, P.; Taqqu, M. S.; Veitch, D., Wavelets for the analysis, estimation, and synthesis of scaling data, (Park, K.; Willinger, W., Self-similar Network Traffic and Performance Evaluation (2000), Wiley), 39-87 |
| [15] | Chechkin, A. V.; Gonchar, V. Y., Chaos, Solitons & Fractals, 12, 391 (2001) · Zbl 0980.60044 |
| [16] | McGaughey, D. R.; Aitken, G. J.M., Physica A, 311, 369 (2002) · Zbl 0996.60091 |
| [17] | Zunino, L.; Pérez, D.; Garavaglia, M.; Rosso, O., Physica A, 379, 503 (2007) |
| [18] | Rosso, O. A.; Zunino, L.; Pérez, D. G.; Figliola, A.; Larrondo, H. A.; Garavaglia, M.; Martín, M. T.; Plastino, A., Phys. Rev. E, 76, 061114 (2007) |
| [19] | Zunino, L.; Pérez, D. G.; Martín, M. T.; Plastino, A.; Garavaglia, M.; Rosso, O. A., Phys. Rev. E, 75, 021115 (2007) |
| [20] | Bandt, C.; Shiha, F., J. Time Ser. Anal., 28, 646 (2007) · Zbl 1150.62037 |
| [21] | Keller, K.; Sinn, M., Physica A, 356, 114 (2005) |
| [22] | Beran, J., Statistics for Long-Memory Processes, Monographs on Statistics and Applied Probability, vol. 61 (1994), Chapman & Hall · Zbl 0869.60045 |
| [23] | Bacon, R. H., Ann. Math. Stat., 34, 191 (1963) · Zbl 0245.62057 |
| [24] | Davies, R. B.; Harte, D. S., Biometrika, 74, 95 (1987) · Zbl 0612.62123 |
| [25] | Wood, A. T.A.; Chan, G., J. Comput. Graph. Stat., 3, 4, 409 (1994) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
