Intermittency expansions for limit lognormal multifractals

Letters in Mathematical Physics

Volumn 83, Issue 3, 2008, Pages 265-280

  Ostrovsky, Dmitry ^a  

^a NONE   (United States)

Author keywords

Intermittency; Multifractal stochastic processes; Riemann zeta; Selberg integral

Indexed keywords

EID: 39849104592     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-008-0225-z     Document Type: Article

References (24)

1. Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (1999)
2. Bacry, E., Delour, J., Muzy, J.-F.: Multifractal random walk. Phys. Rev. E 64, 026103 (2001)
3. Bacry, E., Delour, J., Muzy, J.-F.: Modelling financial time series using multifractal random walks. Physica A 299, 84-92 (2001)
4. Bacry, E., Muzy, J.-F.: Log-infinitely divisible multifractal random walks. Commun. Math. Phys 236, 449-475 (2003)
5. Barral, J., Mandelbrot, B.B.: Multifractal products of cylindrical pulses. Prob. Theory Relat. Fields 124, 409-430 (2002)
6. Calvet, L., Fisher, A.: Multifractality in asset returns: theory and evidence. Rev. Econ. Stat. LXXXIV, 381-406 (2002)
7. Goldberger, A., Amaral, L., Hausdorff, J., Ivanov, P., Peng, C., Stanley, H.: Fractal dynamics in physiology: alterations with disease and aging. Proce. Nat. Acad. Sci. USA 99, 2466-2472 (2002)
8. Ivanov, P., Amaral, L., Goldberger, A., Havlin, S., Rosenblum, M., Struzik, Z., Stanley, H.: Multifractality in human heartbeat dynamics. Nature 399, 461-465 (1999)
9. Kahane, J.-P.: Sur le chaos multiplicatif. Ann. Sci. Math. Que. 9, 105-150 (1985)
10. Kahane, J.-P.: Positive martingales and random measures. Chi. Ann. Math. 8B, 1-12 (1987)
11. Kahane, J.-P.: Produits de poids aléatoires indépendants et applications. In: Belair, J., Dubuc, S. (eds) Fractal Geometry and Analysis, p. 277. Kluwer, Boston (1991)
12. Mandelbrot, B.B.: Possible refinement of the log-normal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. In: Rosenblatt, M., Van Atta, C. (eds) Statistical Models and Turbulence. Lecture Notes in Physics vol 12, p. 333. Springer, New York (1972)
13. Mandelbrot, B.B.: Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331-358 (1974)
14. Mandelbrot, B.B. et al.: Limit lognormal multifractal measures. In: Gotsman, E.A.(eds) Frontiers of Physics: Landau Memorial Conference, p. 309. Pergamon, New York (1990)
15. Meneveau, C., Sreenivasan, K.R.: The multifractal nature of the turbulent energy dissipation. J. Fluid Mech. 224, 429-484 (1991)
16. Muzy, J.-F., Bacry, E.: Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws. Phys. Rev. E 66, 056121 (2002)
17. Ostrovsky, D.: Limit lognormal multifractal as an exponential functional. J. Stat. Phys. 116, 1491-1520 (2004)
18. Ostrovsky, D.: Functional Feynman-Kac equations for limit lognormal multifractals. J. Stat. Phys. 127, 935-965 (2007)
19. Riordan, J.: Combinatorial Identities. Wiley, New York (1968)
20. Schertzer, D., Lovejoy, S.: Physically based rain and cloud modeling by anisotropic, multiplicative turbulent cascades. J. Geophys. Res. 92, 9693-9721 (1987)
21. Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., Marsan, D.: Multifractal cascade dynamics and turbulent intermittency. Fractals 5, 427-471 (1997)
22. Schmitt, F.: A causal multifractal stochastic equation and its statistical properties. Eur. J. Phys. B 34, 85-98 (2003)
23. Schmitt, F., Schertzer, D., Lovejoy, S.: Multifractal analysis of foreign exchange data. Appl. Stoch. Models Data Anal. 15, 29-53 (1999)
24. Selberg, A.: Remarks on a multiple integral. Norske Mat. Tidsskr. 26, 71-78 (1944)