On the physical relevance of max-and log-max-selfsimilar distributions

European Physical Journal B

Volumn 17, Issue 1, 2000, Pages 147-158

  Huillet, T ^a,b   Porzio, A ^c,d   Alaya, M Ben ^c,e  

^a CNRS   (France)

^b UNIVERSITÉ DE CERGY PONTOISE   (France)

^c UNIVERSITÉ PARIS 13   (France)

^d CENTRE DE PHYSIQUE THÉORIQUE   (France)

^e UNIVERSITÉ PARIS EST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006378458     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510070171     Document Type: Article

References (42)

1. Fractals in physics, edited by A. Aharony, J. Feder, Physica D 38 (1-3), (1989).
2. J. Aitchison, J.A.C. Brown, The log-normal distribution (Cambridge University Press, 1957).
3. J.-C. Anifrani, C. Le Floc'h, D. Sornette, B. Souillard, J. Phys. I France 5, 631-638 (1995).
4. A. Arneodo, S. Manneville, J.-F. Muzy, Eur. Phys. J. B 1, 129-140 (1998).
5. A.A. Balkema, S.I. Resnick, J. Appl. Prob. 14, 309-319 (1977).
6. P. Embrechts, C. Klüppelberg, T. Mikosh, Modelling extremal events, Applications of mathematics 33 (Springer-Verlag, 1997).
7. W. Feller, An introduction to probability theory and its applications 2 (Wiley, New York, 1971).
8. U. Frisch, D. Sornette, J. Phys. I France 7, 1155-1171 (1997).
9. J. Galambos, The Asymptotic theory of Extreme Order Statistics (John Wiley and Sons, 1978).
10. B.V. Gnedenko, Ann. Math. 44, 423-453 (1943).
11. I.V. Grinevich, Theory Probab. Appl. 37, 720-721 (1992).
12. I.V. Grinevich, in Stability Problems for Stochastic Models (Perm, TVP/VSP/Moscow/Utrecht, 65-73, 1993).
13. I.V. Grinevich, Theory Probab. Appl. 38, 640-650 (1993).
14. E.J. Gumbel, Statistics of Extremes (Columbia, Columbia University Press, 1958).
15. T. Huillet, H-F. Raynaud, J. Phys. A 32, 1099-1113 (1999).
16. T. Huillet, H.-F. Raynaud, Eur. Phys. J. B 12, 457-469 (1999).
17. A. Johansen, D. Sornette, O. Ledoit, J. Risk 1, 5-32 (1999).
18. A. Johansen, D. Sornette, submitted to the Journal of Risk (1999).
19. A. Johansen, D. Sornette, Int. J. Mod. Phys. C 10, 563-575 (1999).
20. J. Laherrère, D. Sornette, Eur. Phys. J. B 2, 525-539 (1998).
21. J.W. Lamperti, Probability: a survey of mathematical theory, Wiley series in probability and statistics (J. Wiley, NY, 1996).
22. J.W. Lamperti, Trans. Am. Math. Soc. 104, 62-78 (1962).
23. E. Lukacs, Developments in characteristic function theory (C. Griffin and Co. Ltd, London and High Wycombe, 1983).
24. R.A. Maller, S.I. Resnick, Proc. London Math. Soc. 49 385-422 (1984).
25. D. Mejzler, Trans. Amer. Math. Soc. 117, 205-236 (1965).
26. N.R. Mohan, S. Ravi, Theory Probab. Appl. 37, 632-643 (1992).
27. E. Pancheva, J. Math. Sci. 76, 2177-2180 (1995).
28. V. Pareto, Cours d'Economie politique (1896), reprinted as a volume of Oeuvres complètes (Droz, Geneva, 1965).
29. V. Pareto, Cours d'Economie politique (1896), reprinted as a volume of Oeuvres complètes (Droz, Geneva, 1965).
30. W.E. Pruitt, Ann. Prob. 15, 885-896 (1987).
31. S. Ravi, J. Indian Stat. Assoc. 29, 69-77 (1991).
32. S.I. Resnick, Extreme value distributions, regular variations and Point Processes (Springer-Verlag, New York, 1987).
33. H. Saleur, D. Sornette, J. Phys. I France 6, 327-355 (1996).
34. H. Saleur, C.G. Sammis, D. Sornette, Nonlin. Proc. Geophys. 3, 102-109 (1996).
35. H. Saleur, C.G. Sammis, D. Sornette, J. Geophys. Research-Solid Earth 101, 17661-17677 (1996).
36. D. Sornette, Phys. Rep. 297, 239-270 (1998).
37. D. Sornette, L. Knopoff, Y.Y. Kagan, C. Vanneste, J. Geophys. Res. 101, 13883-13893 (1996).
38. D. Sornette, C.G. Sammis, J. Phys. I France 5, 607-619 (1995).
39. D. Sornette, A. Johansen, A. Arneodo, J.-F. Muzy, H. Saleur, Phys. Rev. Lett. 76, 251-254 (1996).
40. D. Sornette, "Discrete scale invariance in turbulence?" in the Proceedings of the Seventh European Turbulence Conference (ETC-7), June 30-July 3 (1998) (Published by Kluwer, U. Frisch, editor).
41. D. Stauffer, D. Sornette, Physica A 271, 496-506 (1999).
42. G.K. Zipf, Human behaviour and the Principle of Least Effort (Addison-Wesley, 1949).