统计自相似测度奇异集的更新
Renewal of singularity sets of statistically self-similar measures
摘要：
研究了一类统计自相似测度的重分形结构的新性质。这些措施包括著名的曼德尔布罗特乘法级联，有时称为独立随机级联。我们评估这些措施的多重分形结构变得可辨的规模。这个尺度的值是通过我们称之为波莱尔测度的霍德尔奇点集的增长速度得到的。这种增长速度产生了新的信息的重标度的副本在统计自相似措施的结构中所涉及的多重分形行为。我们的结果有助于理解各种异质跳跃过程的多重分形性质。
英文摘要：
This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.
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