Advances in Applied Probability

Renewal of singularity sets of random self-similar measures

Julien Barral and Stéphane Seuret

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Abstract

This paper investigates new properties concerning the multifractal structure of a class of random 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 in understanding the multifractal nature of various heterogeneous jump processes.

Article information

Source
Adv. in Appl. Probab. Volume 39, Number 1 (2007), 162-188.

Dates
First available: 30 March 2007

Permanent link to this document
http://projecteuclid.org/euclid.aap/1175266474

Digital Object Identifier
doi:10.1239/aap/1175266474

Zentralblatt MATH identifier
1112.60040

Mathematical Reviews number (MathSciNet)
MR2307876

Subjects
Primary: 60G57: Random measures 60F10: Large deviations 28A78: Hausdorff and packing measures
Secondary: 28A80: Fractals [See also 37Fxx]

Keywords
Random measure large deviations Hausdorff dimension self-similarity fractal

Citation

Barral, Julien; Seuret, Stéphane. Renewal of singularity sets of random self-similar measures. Advances in Applied Probability 39 (2007), no. 1, 162--188. doi:10.1239/aap/1175266474. http://projecteuclid.org/euclid.aap/1175266474.


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