Random cascades on wavelet dyadic trees
Random cascades on wavelet dyadic trees
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DOI：
10.1063/1.532489
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发表时间：
1998-08-01
影响因子：
1.3
通讯作者：
Muzy, JF
中科院分区：
文献类型：
--
作者：
Arneodo, A;Bacry, E;Muzy, JF
利用正交小波变换，我们引入了一类新的随机分形函数。这些函数递归地建立在正交小波变换的空间尺度半平面中，从任意给定的大尺度向小尺度“级联”。每个随机分形函数对应于其正交小波系数的二进树上的随机级联过程（称为W-级联）。通过研究这些级联的奇异谱的支持，我们讨论了这些级联的收敛性以及所获得的随机函数的规律性。然后，我们表明，非常不同的统计量，如相关函数的小波系数或基于小波的多重分形形式主义分区函数可以用来非常精确地表征底层级联过程。我们说明我们所有的结果在各种数值例子。(C)1998年美国物理学会。[S0022-2488（98）01008-1]。
We introduce a new class of random fractal functions using the orthogonal wavelet transform. These functions are built recursively in the space-scale half-plane of the orthogonal wavelet transform, "cascading" from an arbitrary given large scale towards small scales. To each random fractal function corresponds a random cascading process (referred to as a W-cascade) on the dyadic tree of its orthogonal wavelet coefficients. We discuss the convergence of these cascades and the regularity of the so-obtained random functions by studying the support of their singularity spectra. Then, we show that very different statistical quantities such as correlation functions on the wavelet coefficients or the wavelet-based multifractal formalism partition functions can be used to characterize very precisely the underlying cascading process. We illustrate all our results on various numerical examples. (C) 1998 American Institute of Physics. [S0022-2488(98)01008-1].