Multifractal spectra and precise rates of decay in homogeneous fragmentations

By Nathalie Krell. 2006

74 citations recorded by the source corpus.

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 Levy processes constrained to stay in a finite interval.

Subfields: Condensed Matter Physics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b8678c97e3818a366426b3a34f16e29557acf2e3

How researchers see this paper

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In Condensed Matter Physics

1. V. Rivero
2. Alexey Kuznetsov
3. E. Kyprianou
4. Andreas E. Kyprianou
5. Friedrich Hubalek
6. Elie Aidékon
7. Zhan Shi
8. S. Harris

In Finance

1. Andreas E. Kyprianou
2. V. Rivero
3. Alexey Kuznetsov
4. Friedrich Hubalek
5. E. Kyprianou
6. Ronnie Loeffen
7. Chuancun Yin
8. Xiaowen Zhou

In Mathematical Physics

1. V. Rivero
2. Alexey Kuznetsov
3. E. Kyprianou
4. Friedrich Hubalek
5. Andreas E. Kyprianou
6. Zhan Shi
7. Zbigniew Palmowski
8. Ronnie Loeffen

Citations in the corpus

• Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “…Klüppelberg and Kyprianou (2006), Doney and Kyprianou (2006), Kyprianou and Palmowski (2007), Renaud and Zhou (2007), Loeffen (2007) and Kyprianou et al. (2008), in the theory of credit risk Hilberink and Rogers (2002) and Kyprianou and Surya (2007) and in the theory of fragmentation Krell (2007).”
• The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “12) and also built using a scale function, was used by Krell [65] for a more detailed analysis of different rates of fragmentation decay that can occur in the process.”
• Special, conjugate and complete scale functions for spectrally negative Lévy processes (2007, background): “For example, in the theory of optimal stopping [1; 2] and [38], in the theory of optimal control [3], [40; 51] and [44], in the theory of queuing and storage models [21] and [4], in the theory of branching processes [10], [29] and [43], in the theory of insurance risk and ruin [15], [34], [33], [20]”