Multidimensional infinitely divisible cascades

P. Chainais ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 51, issue 2, 229-243

Abstract: The framework of infinitely divisible scaling was first developed to analyse the statistical intermittency of turbulence in fluid dynamics. It also reveals a powerful tool to describe and model various situations including Internet traffic, financial time series, textures ... A series of recent works introduced the infinitely divisible cascades in 1 dimension, a family of multifractal processes that can be easily synthesized numerically. This work extends the definition of infinitely divisible cascades from 1 dimension to d dimensions in the scalar case. Thus, a class of models is proposed both for data analysis and for numerical simulation in dimension d≥1. In this article, we give the definitions and main properties of infinitely divisible cascades in d dimensions. Then we focus on the modelling of statistical intermittency in turbulent flows. Several other applications are considered. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 02.50.Ey Stochastic processes; 05.45.Df Fractals; 47.53.+n Fractals in fluid dynamics; 47.27.E- Turbulence simulation and modelling (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00213-y

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