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.

中文翻译：

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二元乘法级联中的分布不变性

本文设想并证明了在二元乘法级联中级联和“修饰”的组合作用下某些概率分布函数的稳定性特性。它们对于应用的主要重要性在于，考虑到这些级联普遍缺乏分布遍历性，从单一实现中对多重分形测度的乘法级联生成器进行参数化。数值模拟也说明了结果。