Multifractal Analysis of Choquet Capacities

Advances in Applied Mathematics

Volumn 20, Issue 1, 1998, Pages 1-43

  Véhel, Jacques Lévy ^a   Vojak, Robert ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001239909     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1996.0517     Document Type: Article

References (27)

1. Mandelbrot B. B. Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. Statistical Models and Turbulence (La Jolla, CA 1972). Lecture Notes in Physics. 12:1972;Springer-Verlag, New York. p. 331-351.
2. Mandelbrot B. B. Intermittent turbulence in self similar cascades: Divergence of high moments and dimension of the carrier. J. Fluid Mech. 62:1974;331-358.
3. Mandelbrot B. B. Multifractal measures, especially for the geophysicist. Pure Appl. Geophys. 131:1989;5-42.
4. Mandelbrot B. B. A class of multinomial multifractal measures with negative (latent) values for the dimensionf. Pietronero L. Fractals' Physical Origin and Properties (Erice, 1988). 1989;3-29 Plenum, New York.
5. Mandelbrot B. B. Limit lognormal multifractal measures. Gostman E. A. Frontiers of Physics; Landau Memorial Conference, (Tel Aviv, 1988). 1990;309-340 Pergamon, Elmsford.
6. Frisch U., Parisi G. Ghil M., Benzi R., Parisi G. Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. 1985;84 North-Holland, Amsterdam.
7. Hasley T. C., Jensen M. H., Kadanoff L. P., Procaccia I., Shraiman B. I. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. February 1986.
8. Mandelbrot B. B. Multiplications aléatoires itérées et distributions invariantes par moyenne pondérée aléatoire. C.R. Acad. Sci. Paris Ser. A. 278:1974;289-292.
9. Mandelbrot B. B. Multiplications aléatoires itérées et distributions invariantes par moyenne pondérée aléatoire: Quelques extensions. C.R. Acad. Sci. Paris Ser. A. 278:1974;355-358.
10. Mandelbrot B. B. Random multifractals: Negative dimensions and the resulting limitations of the thermodynamical formalism. Proc. Roy. Soc. London Ser. A. 434:1991;79-88.
11. Evertsz C. J. G., Mandelbrot B. B. Multifractal measures. Peitgen H.-O., Jürgens H., Saupe D. Chaos and Fractals: New Frontiers in Science. 1992;849-881 Springer-Verlag, New York.
12. B. B. Mandelbrot, Negative dimensions and Hölders, multifractals, and the role of lateral preasymptotics in science, in, Fourier Analysis and Applications, Paris, 1993 (J. P. Kahane Meeting), J. Peyrière.
13. Falconer K. J. The multifractal spectrum of statistically self-similar measures. Journal of Theoret. Probab. 7:1994;681-702.
14. Brown G., Michon G., Peyrière J. On the multifractal analysis of measures. J. Statist. Phys. 66:1992;775-790.
15. Holley R., Waymire E. Multifractal dimensions and scaling exponents for strongly bounded random cascades. Ann. Appl. Probab. 2:1992;819-845.
16. M. Arbeiter, N. Patzschke, Random self-similar multifractal, Adv. in Math.
17. Deheuvels P. Fractales aléatoires générées par des processus empiriques. Ann. Probab. 1994.
18. Olsen L. Random Geometrically Graph Directed Self-Similar Multifractals. Pitman Research Notes in Mathematics. 307:1994;Pitman, London.
19. E. Bacry, J.-F. Muzy, A. Arneodo, Singularity spectrum of fractal signal from wavelet analysis: Exact results, J. Statist. Phys.
20. Jaffard S. Construction de fonctions multifractales ayant un spectre de singularites prescrit. C.R. Acad. Sci. Paris Ser. I. 315:1992;19-24.
21. Véhel J. Lévy, Mignot P. Multifractal segmentation of images. Fractals. 2:1994;371-377.
22. J. Lévy, Véhel, J.-P. Berroir, Image analysis through multifractal description, in, Fractal, 1993, Londres, 1993.
23. Dellacherie C. Capacités et processus stochastiques. 1972;Springer-Verlag, Berlin/New York.
24. Billingsley P. Ergodic Theory and Information. 1978;Krieger, Melbourne.
25. Peyrière J. Calculs de dimensions de Hausdorff. Duke Math. J. 44:1977;591-601.
26. R. Riedi, An improved multifractal formalism and self-similar measures, J. Math. Anal. Appl.
27. Pólya G., Szegö G. Problems and Theorems in Analysis. 1972.