This article is cited in 5 papers

MISCELLANEOUS

Numerical simulation of the realizations and spectra of a quasi-multifractal diffusion process

A. I. Saichev, V. A. Filimonov

Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

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.

PACS: 02.50.-r, 05.40.-a, 05.45.Df, 47.53.+n

Received: 11.02.2008
Revised: 25.03.2008

 English version: Journal of Experimental and Theoretical Physics Letters, 2008, 87:9, 506–510

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