Analysis of random cascades using space-scale correlation functions

Physical Review Letters

Volumn 80, Issue 4, 1998, Pages 708-711

  Arneodo, A ^a   Bacry, E ^b   Manneville, S ^a   Muzy, J F ^a  

^a CENTRE DE RECHERCHE PAUL PASCAL   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001041932     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.80.708     Document Type: Article

References (31)

1. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
2. M. Ghil, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985), p. 84.
3. T. C. Halsey et al., Phys. Rev. A 33, 1141 (1986).
4. G. Paladin and A. Vulpiani, Phys. Rep. 156, 147 (1987).
5. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989);
6. A. L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
7. C. Meneveau and K. R. Sreenivasan, J. Fluid Mech. 224, 429 (1991).
8. H. G. E. Hentschel, Phys. Rev. E 50, 243 (1994).
9. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2.
10. A. N. Kolmogorov, C.R. Acad. Sci. USSR 30, 301 (1941);
11. A. N. Kolmogorov J. Fluid Mech. 13, 82 (1962).
12. A. M. Obukhov, J. Fluid Mech. 13, 77 (1962).
13. B. B. Mandelbrot, J. Fluid Mech. 62, 331 (1974).
14. E. A. Novikov, Phys. Fluids A 2, 814 (1990);
15. E. A. Novikov Phys. Rev. E 50, 3303 (1994).
16. U. Frisch, Turbulence (Cambridge University Press, Cambridge, England, 1995).
17. B. Castaing, Y. Gagne, and E. J. Hopfinger, Physica (Amsterdam) 46D, 177 (1990);
18. B. Chabaud et al., Phys. Rev. Lett. 73, 3227 (1994);
19. B. Castaing and B. Dubrulle, J. Phys. II (France) 5, 895 (1995).
20. M. E. Cates and J. M. Deutsch, Phys. Rev. A 35, 4907 (1987);
21. R. Julien, L. Peliti, R. Rammal, and N. Boccara (Springer-Verlag, Heidelberg, 1988), p. 188;
22. J. O'Neil and C. Meneveau, Phys. Fluids A 5, 158 (1993).
23. J. F. Muzy, E. Bacry, and A. Arneodo, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 245 (1994);
24. A. Arneodo, E. Bacry, and J. F. Muzy, Physica (Amsterdam) 213A, 232 (1995).
25. Y. Meyer, Ondelettes (Hermann, Paris, 1990);
26. I. Daubechies, Ten Lectures on Wavelets (S.I.A.M., Philadelphia, 1992).
27. F. Moret-Bailly et al., C.R. Acad. Sci. Ser. 2 313, 591 (1991).
28. R. Benzi et al., Physica (Amsterdam) 65D, 352 (1993);
29. A. Arneodo et al., J. Fourier Anal. Appl. (to be published).
30. A. Arneodo, J. F. Muzy, and S. G. Roux, J. Phys. II (France) 7, 363 (1997).
31. A. Arneodo, J. F. Muzy, and D. Sornette, “Causal Cascade in the Stock Market from the Infrared to the Ultraviolet” (to be published).