Abstract
A quasi-multifractal model of stochastic processes is considered. In contrast to the more widely known multifractal random walk model, it is free of such substantial drawbacks as infinite variance of the modeled processes and time-dependent increments. An analysis of a multifractal diffusion-type process is presented, including the moments of increments and local scaling exponents of the process. A quasi-multifractal spectrum of the process is computed. A focus is on two new concepts in the theory of multifractal processes: effective scaling exponent and quasi-multifractal spectrum of a process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 99 (1941).
B. B. Mandelbrot, On Intermittent Free Turbulence, Turbulence of Fluids and Plasmas (Interscience, New York, 1969).
B. Pochart and J.-P. Bouchaud, Quantitative Finance 2, 303 (2002).
E. Bacry, J. Delour, and J.-F. Muzy, Phys. Rev. E 64,026103 (2001).
E. Bacry, J. Delour, and J.-F. Muzy, cond-mat/0009260.
E. Bacry and J.-F. Muzy, Commun. Math. Phys. 236, 449 (2003).
A. Saichev and D. Sornette, Phys. Rev. E 74, 011111-1 (2006).
E. A. Novikov, Phys. Fluids A 2, 814 (1990).
R. Friedrich and J. Peinke, Phys. Rev. Lett. 78, 863 (1997).
B. Castaing, Y. Gagne, and E. Hopfinger, Physica D (Amsterdam) 46, 177 (1990).
D. Sornette, Y. Malevergne, and J.-F. Muzy, Risk 16, 67 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Saichev, V.A. Filimonov, 2007, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 132, No. 5, pp. 1235–1244.