On Multifractality and Fractional Derivatives View Full Text


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Article Info

DATE

2002-09

AUTHORS

U. Frisch, T. Matsumoto

ABSTRACT

It is shown phenomenologically that the fractional derivative ξ = Dαu of order α of a multifractal function has a power-law tail ∝ in its cumulative probability, for a suitable range of α's. The exponent is determined by the condition , where ζp is the exponent of the structure function of order p. A detailed study is made for the case of random multiplicative processes (Benzi et al., Physica D65:352 (1993)) which are amenable to both theory and numerical simulations. Large deviations theory provides a concrete criterion, which involves the departure from straightness of the ζp graph, for the presence of power-law tails when there is only a limited range over which the data possess scaling properties (e.g., because of the presence of a viscous cutoff). The method is also applied to wind tunnel data and financial data. More... »

PAGES

1181-1202

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URI

http://scigraph.springernature.com/pub.10.1023/a:1019843616965

DOI

http://dx.doi.org/10.1023/a:1019843616965

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133 https://www.grid.ac/institutes/grid.440460.2 schema:alternateName Observatoire de la Côte d’Azur
134 schema:name Observatoire de la Côte d'Azur, CNRS UMR 6529, BP 4229, 06304, Nice Cedex 4, France
135 rdf:type schema:Organization
 




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