Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 24, 2008, Pages 6057-6068

  Zunino, L ^a,b,c   Perez D G ^d   Kowalski, A ^e,f   Martin M T ^e,g   Garavaglia, M ^a,c   Plastino, A ^e,g   Rosso, O A ^h,i  

^a CENTRO DE INVESTIGACIONES OPTICAS   (Argentina)

^b UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^c FACULTAD DE CIENCIAS EXACTAS   (Argentina)

^d PONTIFICIA UNIVERSIDAD CATÓLICA DE VALPARAÍSO   (Chile)

^e INSTITUTO DE FÍSICA LA PLATA   (Argentina)

^f Universidad Provincial del Sudoeste   (Argentina)

^g Facultad de Ciencias Naturales e Instituto M Lillo   (Argentina)

^h UNIVERSITY OF NEWCASTLE   (Australia)

ⁱ INSTITUTO DE CÁLCULO   (Argentina)

Author keywords

Bandt Pompe method; Fractional Brownian motion; Fractional Gaussian noise; Tsallis entropy

Indexed keywords

BROWNIAN MOVEMENT; GAUSSIAN NOISE (ELECTRONIC); RISK ASSESSMENT; STOCHASTIC PROGRAMMING; TRELLIS CODES;

ENTROPIC INDEXES; FRACTIONAL BROWNIAN MOTION; FRACTIONAL GAUSSIAN NOISE; OPTIMUM VALUE; PERMUTATION ENTROPY; POW ERFUL TOOL; RANGES OF VALUES; STOCHASTIC PROCESSING; TSALLIS ENTROPY;

PROBABILITY DISTRIBUTIONS;

EID: 49649083517     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.07.004     Document Type: Article

References (39)

1. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52 (1988) 479-487
2. Havrda J., and Chárvat F. Quantification methods of classification processes: Concepts of structural α-entropy. Kybernetica 3 (1967) 30-35
3. Daróczy Z. Generalized information functions. Inf. Control 16 (1970) 36-51
4. Alemany P.A., and Zanette D.H. Fractal random walks from a variational formalism for Tsallis entropies. Phys. Rev. E 49 2 (1994) R956-R958
5. Tsallis C. Nonextensive thermostatistics and fractals. Fractals 3 3 (1995) 541-547
6. Capurro A., Diambra L., Lorenzo D., Macadar O., Martin M.T., Mostaccio C., Plastino A., Rofman E., Torres M.E., and Velluti J. Tsallis entropy and cortical dynamics: The analysis of EEG signals. Physica A 257 (1998) 149-155
7. Tong S., Bezerianos A., Paul J., Zhu Y., and Thakor N. Nonextensive entropy measure of EEG following brain injury from cardiac arrest. Physica A 305 (2002) 619-628
8. Tsallis C., Anteneodo C., Borland L., and Osorio R. Nonextensive statistical mechanics and economics. Physica A 324 1-2 (2003) 89-100
9. Rosso O.A., Martín M.T., and Plastino A. Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures. Physica A 320 (2003) 497-511
10. Borland L. Long-range memory and nonextensivity in financial markets. Europhys. News 36 (2005) 228-231
11. Huang H., Xie H., and Wang Z. The analysis of VF and VT with wavelet-based Tsallis information measure. Phys. Lett. A 336 (2005) 180-187
12. Pérez D.G., Zunino L., Martín M.T., Garavaglia M., Plastino A., and Rosso O.A. Model-free stochastic processes studied with q-wavelet-based informational tools. Phys. Lett. A 364 (2007) 259-266
13. Kalimeri M., Papadimitriou C., Balasis G., and Eftaxias K. Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy. Physica A 387 (2008) 1161-1172
14. Tsallis C. Generalized entropy-based criterion for consistent testing. Phys. Rev. E 58 (1998) 1442-1445
15. Bandt C., and Pompe B. Permutation entropy: A natural complexity measure for time series. Phys. Rev. Lett. 88 (2002) 174102
16. Keller K., and Lauffer H. Symbolic analysis of high-dimensional time series. Internat. J. Bifur. Chaos 13 (2003) 2657-2668
17. Cao Y., Tung W., Gao J.B., Protopopescu V.A., and Hively L.M. Detecting dynamical changes in time series using the permutation entropy. Phys. Rev. E 70 (2004) 046217
18. Larrondo H.A., González C.M., Martín M.T., Plastino A., and Rosso O.A. Intensive statistical complexity measure of pseudorandom number generators. Physica A 356 (2005) 133-138
19. Larrondo H.A., Martín M.T., González C.M., Plastino A., and Rosso O.A. Random number generators and causality. Phys. Lett. A 352 (2006) 421-425
20. Kowalski A., Martín M.T., Plastino A., and Rosso O.A. Bandt-Pompe approach to the classical-quantum transition. Physica D 233 (2007) 21-31
21. Rosso O.A., Larrondo H.A., Martín M.T., Plastino A., and Fuentes M.A. Distinguishing noise from chaos. Phys. Rev. Lett. 99 (2007) 154102
22. Rosso O., Vicente R., and Mirasso C. Encryption test of pseudo-aleatory messages embedded on chaotic laser signals: An information theory approach. Phys. Lett. A 372 (2008) 1018-1023
23. Li X., Ouyang G., and Richards D.A. Predictability analysis of absence seizures with permutation entropy. Epilepsy Res. 77 (2007) 70-74
24. Mandelbrot B.B. The Fractal Geometry of Nature (1982), W. H. Freeman, New York
25. Voss R.F. Evolution of long-range fractal correlations and 1 / f noise in DNA base sequences. Phys. Rev. Lett. 68 (1992) 3805-3808
26. Allegrini P., Buiatti M., Grigolini P., and West B.J. Fractional Brownian motion as a nonstationary process: An alternative paradigm for DNA sequences. Phys. Rev. E 57 (1998) 4558-4567
27. Su Z.-Y., and Wu T. Music walk, fractal geometry in music. Physica A 380 (2007) 418-428
28. Abry P., Flandrin P., Taqqu M.S., and Veitch D. Wavelets for the analysis, estimation, and synthesis of scaling data. In: Park K., and Willinger W. (Eds). Self-similar Network Traffic and Performance Evaluation (2000), Wiley 39-87
29. Chechkin A.V., and Gonchar V.Y. Fractional Brownian motion approximation based on fractional integration of a white noise. Chaos Solitons Fractals 12 (2001) 391-398
30. McGaughey D.R., and Aitken G.J.M. Generating two-dimensional fractional Brownian motion using the fractional Gaussian process (FGp) algorithm. Physica A 311 (2002) 369-380
31. Zunino L., Pérez D., Garavaglia M., and Rosso O. Wavelet entropy of stochastic processes. Physica A 379 (2007) 503-512
32. Rosso O.A., Zunino L., Pérez D.G., Figliola A., Larrondo H.A., Garavaglia M., Martín M.T., and Plastino A. Extracting features of Gaussian self-similar stochastic processes via the Bandt & Pompe approach. Phys. Rev. E 76 (2007) 061114
33. Zunino L., Pérez D.G., Martín M.T., Garavaglia M., Plastino A., and Rosso O.A. Permutation entropy of fractional Brownian motion and fractional Gaussian noise. Phys. Lett. A 372 (2008) 4768-4774
34. Keller K., and Sinn M. Ordinal analysis of time series. Physica A 356 (2005) 114-120
35. Zunino L., Pérez D.G., Martín M.T., Plastino A., Garavaglia M., and Rosso O.A. Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools. Phys. Rev. E 75 (2007) 021115
36. Beran J. Statistics for long-memory processes. Monographs on Statistics and Applied Probability vol. 61 (1994), Chapman & Hall
37. Bandt C., and Shiha F. Order patterns in time series. J. Time Ser. Anal. 28 (2007) 646-665
38. Davies R.B., and Harte D.S. Tests for Hurst effect. Biometrika 74 (1987) 95-102
39. d. J. Comput. Graph. Statist. 3 4 (1994) 409-432