Multifractal spectra and precise rates of decay in homogeneous fragmentations

Nathalie Krell

Stochastic Processes and their Applications, 2008, vol. 118, issue 6, 897-916

Abstract: We consider a mass-conservative fragmentation of the unit interval. Motivated by a result of Berestycki [J. Berestycki, Multifractal spectra of fragmentation processes, J. Statist. Phys. 113 (3-4) (2003) 411-430], the main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale which arises naturally in this setting, and a class of Lévy processes constrained to stay in a finite interval.

Keywords: Interval; fragmentation; Lévy; process; Multifractal; spectrum (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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