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Renewal of singularity sets of statistically self-similar measures

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00004527
Contributor : Stephane Seuret Connect in order to contact the contributor
Submitted on : Monday, March 21, 2005 - 2:00:09 PM
Last modification on : Friday, March 11, 2022 - 4:20:02 PM
Long-term archiving on: : Thursday, April 1, 2010 - 9:03:21 PM

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Julien Barral, Stephane Seuret. Renewal of singularity sets of statistically self-similar measures. 2005. ⟨hal-00004527⟩

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