Multifractal analysis in a mixed asymptotic framework. (English) Zbl 1252.60036
This article deals with multifractal processes. In the literature, this kind of process has been used in many applications, for example, in order to model the velocity or the dissipation in a fully developed turbulence. A multifractal distribution of points generated by a random process is called multiplicative random cascade. A lot of studies have been dedicated to this field, especially in studying the partition function of a cascade, which entirely represents its multifractal properties. The definitions and the properties of cascades are stated at the beginning of the paper.
The main results in the literature usually concern the study of one single cascade. The authors in this work adopt an approach in which the number of cascade realizations becomes infinity showing interesting properties of the partition function. The convergence properties and the estimator of the cumulant generating function are studied. In the last section of the work, the authors present some specific example in order to illustrate the results.
The main results in the literature usually concern the study of one single cascade. The authors in this work adopt an approach in which the number of cascade realizations becomes infinity showing interesting properties of the partition function. The convergence properties and the estimator of the cumulant generating function are studied. In the last section of the work, the authors present some specific example in order to illustrate the results.
Reviewer: Enzo Orsingher (Roma)
MSC:
| 60G18 | Self-similar stochastic processes |
| 60G57 | Random measures |
| 60F99 | Limit theorems in probability theory |
Keywords:
multifractal processes; multifractal formalism; random cascades; scaling exponents estimation; Besov spaceReferences:
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