Multifractal products of cylindrical pulses

Probability Theory and Related Fields

Volumn 124, Issue 3, 2002, Pages 409-430

  Barral, Julien ^a   Mandelbrot, Benoît B ^b  

^a INRIA ROCQUENCOURT   (France)

^b YALE UNIVERSITY   (United States)

Author keywords

Continuous time martingales; Multifractal analysis; Random measures; Statistically self similar Poisson point processes

Indexed keywords

EID: 0036026998     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400200220     Document Type: Article

References (20)

1. [B1] Barral, J.: Moments, continuité, et analyse multifractale des martingales de Mandelbrot, Probab. Theory Relat. Fields, 113, 535-569 (1999)
2. [B2] Barral, J.: Continuity of the multifractal spectrum of a statistically self-similar measure, J. Theoretic. Probab., 13, 1027-1060 (2000)
3. [BM] Barral, J., Mandelbrot, B.B.: Products of non-cylindrical pulses, to appear in "Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot". Proc. of the Special Session held at the Annual Meeting of the American Mathematical Society in San Diego, California, January 6-7, 2002. Edited by M.L. Lapidus, M. van Frankenhuysen. American Mathematical Society, Providence, RI.
4. [Bi] Biggins, J.D.: Uniform convergence of martingales in the branching random walk, Ann. Probab., 20, 137-151 (1992)
5. [BMP] Brown, G., Michon, G., Peyrière, J.: On the multifractal analysis of measures, J. Stat. Phys., 66, 775-790 (1992)
6. [F] Falconer, K.J.: Techniques in Fractal Geometry. Wiley (1997)
7. [HoWa] Holley, R., Waymire, E.C.: Multifractal dimensions and scaling exponents for strongly bounded random fractals, Ann. Appl. Probab., 2, 819-845 (1992)
8. [K1] Kahane, J.-P.: Positive martingales and random measures, Chi. Ann. Math., 8B, 1-12 (1987)
9. [K2] Kahane, J.-P.: Produits de poids aléatoires et indépendants et applications, in Fractal Geometry and Analysis, J. Bélair, S. Dubuc (eds.) pp. 277-324 (1991)
10. [KP] Kahane, J.-P., Peyrière, J.: Sur certaines martingales de Benoît Mandelbrot, Adv. Math., 22, 131-145 (1976). Translation in [Ma7]
11. [Ma1] Mandelbrot, B.B.: Possible refinement of the lognormal hypothesis concerning the distribution of energy in intermittent turbulence. Statistical Models and Turbulence (La Jolla, California). Edited by M. Rosenblatt, C. Van Atta, Lectures Notes in Physics, Vol. 12, Springer, New York (1972) pp. 333-351. Reprint in [Ma7]
12. [Ma2] Mandelbrot, B.B.: Renewal sets and random cutouts, Z. Wahrsch. Verw. Geb., 22, 145-157 (1972)
13. [Ma3] Mandelbrot, B.B.: Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the cagier, J. Fluid. Mech., 62, 331-358 (1974). Reprint in [Ma7]
14. [Ma4] Mandelbrot, B.B.: Multiplications aléatoires itérées et distributions invariantes par moyennes pondérées, C. R. Acad. Sci. Paris, 278, 289-292, 355-358 (1974). Translation in [Ma7]
15. [Ma5] Mandelbrot, B.B.: Introduction to fractal sums of pulses. Lévy Flights and Related Phenomena in Physics (Nice, 1994). Edited by G. Zaslawsky, M.F. Shlesinger, U. Frisch, Lectures Notes in Physics, Springer, New York (1995)
16. [Ma6] Mandelbrot, B.B.: Multifractal products of pulses, unpublished memorandum (1996)
17. [Ma7] Mandelbrot, B.B.: Multifractals and 1/f Noise, Springer, New York (1999)
18. [Mol] Molchan, G.M.: Scaling exponents and multifractal dimensions for independent random cascades, Commun. Math. Phys., 179, 681-702 (1996)
19. [O] Olsen, L.: A multifractal formalism, Adv. Math., 116, 92-195 (1995)
20. [WaWi] Waymire, E.C., Williams, S.C.: A cascade decomposition theory with applications to Markov and exchangeable cascades, Trans. Am. Math. Soc., 348, 585-632 (1996)