二元乘法级联的分布不变性

Fractals Pub Date : 2024-04-30 DOI:10.1142/s0218348x24500725

CÉSAR AGUILAR-FLORES, ALIN-ANDREI CARSTEANU

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摘要

本文考虑并证明了某些概率分布函数在二元乘法级联的级联和 "敷料 "共同作用下的稳定性。鉴于这些级联一般缺乏分布遍历性，它们在应用中的主要重要性在于从单一实现中为多分形度量的乘法级联生成器确定参数。这些结果也将通过数值模拟加以说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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DISTRIBUTIONAL INVARIANCE IN BINARY MULTIPLICATIVE CASCADES

The stability properties of certain probability distribution functions under the combined effects of cascading and “dressing” in a binary multiplicative cascade are contemplated and proven herein. Their main importance for applications resides in parameterizing the multiplicative cascade generators of multifractal measures from single realizations, given the generic lack of distributional ergodicity of those cascades. The results are also being illustrated by numerical simulations.

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Fractals

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