A Unified Framework for the Study of the 2-microlocal and Large Deviation Multifractal Spectra
| Autor: | Echelard, Antoine, Lévy Véhel, Jacques, Tricot, Claude |
|---|---|
| Přispěvatelé: | Probabilistic modelling of irregularity and application to uncertainties management ( Regularity ), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathématiques Appliquées aux Systèmes - EA 4037 (MAS), Ecole Centrale Paris, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), SMF |
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Self similar processes and their applications Self similar processes and their applications, SMF, Jul 2009, Angers, France. pp.13-44 |
| Popis: | International audience; The large deviation multifractal spectrum is a function of central importance in multifractal analysis. It allows a ne description of the distribution of the singularities of a function over a given domain. The 2-microlocal spectrum, on the other hand, provides an extremely precise picture of the regularity of a distribution at a point. These two spectra display a number of similarities: their de nitions use the same kind of ingredients; both functions are semi-continuous; the Legendre transform of the two spectra yields a function of independent interest: the 2-microlocal frontier in 2-microlocal analysis, and the "\tau " function in multifractal analysis. This paper investigates further these similarities by providing a common framework for the de nition and study of the spectra. As an application, we obtain slightly generalized versions of the 2-microlocal and weak multifractal formalisms (with simpler proofs), as well as results on the inverse problems for both spectra. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|