Multidimensional infinitely divisible cascades |
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Authors: | P Chainais |
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Institution: | (1) LIMOS UMR CNRS 6158-Université Blaise Pascal, 63173 Aubière Cedex, France |
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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. |
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Keywords: | 02 50 Ey Stochastic processes 05 45 Df Fractals 47 53 +n Fractals in fluid dynamics 47 27 E- Turbulence simulation and modelling |
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