Abstract
A discrete model has been developed for a quasi-multifractal diffusion process and a new method for calculating the quasi-multifractal spectrum has been proposed with the use of the statistical processing of the realizations of the process. This method makes it possible to obtain an almost continuous process spectrum, which is impossible by means of traditional analytical methods. The numerical experiments indicate three significantly different regions of the parameters: regions of “monofractality,” “tempered” multifractality, and “strong” multifractality. The model allows deeper insight into the mechanisms of multifractal phenomena in strong turbulence and in the stochastic behavior of financial markets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. F. Richardson, Weather Prediction by Numerical Process (Cambridge Univ., Cambridge, 1922).
A. N. Kolmogorov, Dokl. Akad. Nauk 31, 99 (1941).
U. Frish, Turbulence, The Legacy of A.N. Kolmogorov (Cambridge Univ., Cambridge, 1995).
R. Friedrich and J. Peinke, Phys. Rev. Lett. 78, 863 (1997).
M. Alber, S. Lueck, C. Renner, et al., nlin/0007014 (1998).
V. Yakhota and K. R. Sreenivasan, Physica A 343, 147 (2004).
L. Biferale, G. Boffetta, A. Celani, et al., Phys. Rev. Lett. 93, 064502 (2004).
U. Frisch, M. M. Afonso, A. Mazzino, et al., J. Fluid Mech. 542, 97 (2005).
L. Chevillard, B. Castaing, E. Leveque, et al., Physica D 218, 77 (2006).
B. Pochart and J.-P. Bouchaud, Quantitative Finance 2, 303 (2002).
L. Borland, J.-P. Bouchaud, J.-F. Muzy, and G. Zumbach, cond-mat/0501292 (2005).
E. A. Novikov, Phys. Fluids A 2, 814 (1990).
B. Castaing, Y. Gagne, and E. Hopfinger, Physica D 46, 177 (1990).
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 (2000).
A. Saichev and D. Sornette, Phys. Rev. E 74, 011111-1 (2006).
A. I. Saichev and V. A. Filimonov, Zh. Eksp. Teor. Fiz. 132, 1235 (2007) [JETP 105, 1085 (2007)].
M. Matsumoto and T. Nishimura, ACM Trans. Modell. Comp. Simul. 8, 3 (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Saichev, V.A. Filimonov, 2008, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 87, No. 9, pp. 592–596.
Rights and permissions
About this article
Cite this article
Saichev, A.I., Filimonov, V.A. Numerical simulation of the realizations and spectra of a quasi-multifractal diffusion process. Jetp Lett. 87, 506–510 (2008). https://doi.org/10.1134/S0021364008090129
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364008090129