Generalized (m, k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend

International Journal of Modern Physics C

Volumn 14, Issue 3, 2003, Pages 351-365

  Bronlet, Ph ^a   Ausloos, M ^a  

^a SUPRAS and GRASP   (Belgium)

Author keywords

Fractional Brownian motion; Hurst exponent; Trend; Zipf

Indexed keywords

EID: 0037967215     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183103004528     Document Type: Article

References (50)

1. G. K. Zipf, Human Behavior and the Principle of Least Effort (Addisson-Wesley, Cambridge, MA, 1949).
2. B. J. West and W. Deering, Phys. Rep. 246, 1 (1994); B. J. West and B. Deering, The Lure of Modern Science: Fractal Thinking (World Scientific, Singapore, 1995).
3. B. J. West and W. Deering, Phys. Rep. 246, 1 (1994); B. J. West and B. Deering, The Lure of Modern Science: Fractal Thinking (World Scientific, Singapore, 1995).
4. B. Hill, J. Am. Stat. Assoc. 69, 1017 (1974).
5. B. Hill and M. Woodroofe, J. Am. Stat. Assoc. 70, 212 (1975).
6. M. A. Montemurro, Physica A 300, 567 (2001).
7. V. Pareto, Cours d'Économie Politique (Droz, Geneva, 1896).
8. B. Mandelbrot, Intern. Econ. Rev. 1, 79 (1960).
9. K. Okuyama, M. Takayasu, and H. Takayasu, Physica A 269, 125 (1999).
10. M. H. R. Stanley, S. V. Buldyrev, S. Havlin, R. Mantegna, M. A. Salinger, and H. E. Stanley, Econom. Lett. 49, 453 (1995).
11. J. J. Ramsden and Gy. Kiss-Haypál, Physica A 277, 220 (2000).
12. B. Gutenberg and R. F. Richter, Bull. Seis. Soc. Amer. 34, 185 (1944).
13. D. Sornette, L. Knopoff, Y. Y. Kagan, and C. Vanneste, J. Geophys. Res. 101, 13883 (1996).
14. M. Marsili and Y.-C. Zhang, Phys. Rev. Lett. 80, 2741 (1998).
15. X. Gabaix, Quart. J. Econ. 114, 739 (1999); X. Gabaix, Am. Econ. Rev. Papers Proc. 89, 129 (1999).
16. X. Gabaix, Quart. J. Econ. 114, 739 (1999); X. Gabaix, Am. Econ. Rev. Papers Proc. 89, 129 (1999).
17. Y. G. Ma, Eur. Phys. J. A 6, 367 (1999).
18. J. R. Piqueira, L. H. Monteiro, T. M. de Magalhaes, R. T. Ramos, R. B. Sassi, and E. G. Cruz, J. Theor. Biol. 198, 439 (1999).
19. W. Li, "Zipf's law in importance of genes for cancer classification using microarray data," arxiv.org e-print, physics/0104028.
20. J. Kalda, M. Sakki, M. Vainu, and M. Laan, "Zipf's law in human heatbeat dynamics," arxiv.org e-print, physics/0110075.
21. N. Vandewalle and M. Ausloos, Physica A 268, 240 (1999).
22. M. Ausloos and K. Ivanova, Physica A 270, 526 (1999).
23. M. Ausloos, Physica A 285, 48 (2000).
24. N. Vandewalle, Ph. Boveroux, and F. Brisbois, Eur. Phys. J. B 15, 547 (2000).
25. A. Czirok, H. E. Stanley, and T. Vicsek, Phys. Rev. E 53, 6371 (1996).
26. K. Kawamura and N. Hatano, "Universality of Zipf's law," cond-mat/0203455.
27. A. G. Ellinger, The Art of Investment (Bowers & Bowers, London, 1971).
28. P. S. Addison, Fractals and Chaos (Institute of Physics, Bristol, 1997).
29. H. E. Hurst, Trans. Amer. Soc. Civil Eng. 116, 770 (1951).
30. E. E. Peters, Fractal Market Analysis: Applying Chaos Theory to Investment and Economics (Wiley Finance Editions, New York, 1994).
31. E. E. Peters, Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility (Wiley Finance Editions, New York, 1996).
32. S. Rambaldi and O. Pinazza, Physica A 208, 21 (1994).
33. A. Pekalski (ed.), Diffusion Processes: Experiment, Theory, Simulations (Springer Verlag, Berlin, 1994).
34. A. Czirok, R. N. Mantegna, S. Havlin, and H. E. Stanley, Phys. Rev. E 52, 446 (1995).
35. G. Troll and P. B. Graben, Phys. Rev. E 57, 1347 (1998).
36. M. Ya. Azbel, Phys. Rev. Lett. 75, 168 (1995).
37. C. K. Peng, S. Buldyrev, A. Goldberger, S. Havlin, F. Sciortino, M. Simons, and H. E. Stanley, Physica A 191, 25 (1992); H. E. Stanley, S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, and M. Simons, Physica A 200, 4 (1993); S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Masta, C.-K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E 51, 5084 (1995).
38. C. K. Peng, S. Buldyrev, A. Goldberger, S. Havlin, F. Sciortino, M. Simons, and H. E. Stanley, Physica A 191, 25 (1992); H. E. Stanley, S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, and M. Simons, Physica A 200, 4 (1993); S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Masta, C.-K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E 51, 5084 (1995).
39. C. K. Peng, S. Buldyrev, A. Goldberger, S. Havlin, F. Sciortino, M. Simons, and H. E. Stanley, Physica A 191, 25 (1992); H. E. Stanley, S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, and M. Simons, Physica A 200, 4 (1993); S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Masta, C.-K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E 51, 5084 (1995).
40. N. Vandewalle and M. Ausloos, Physica A 246, 454 (1997).
41. M. Ausloos, N. Vandewalle, Ph. Boveroux, A. Minguet, and K. Ivanova, Physica A 274, 229 (1999).
42. K. Ivanova and M. Ausloos, Physica A 274, 349 (1999).
43. K. Ivanova, M. Ausloos, E. E. Clothiaux, and T. P. Ackerman, Europhys. Lett. 52, 40 (2000).
44. http://www.hpl.hp.com/shl/papers/ranking/ranking.html.
45. J. D. Gibbons, Nonparametric Methods for Quantitative Analysis, 2nd Edition (America Sciences Press, Columbus, OH, 1985).
46. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997).
47. Y.-C. Zhang, Physica A 269, 30 (1999).
48. L. Molgedey and W. Ebeling, Eur. Phys. J. B 15, 733 (2000).
49. M. Ausloos and Ph. Bronlet, IEC02 Proceedings, unpublished.
50. K. Hu, P. Ch. Ivanov, Z. Chen, P. Carpena, and H. E. Stanley, Phys. Rev. E 64, 11114 (2001).