On various multifractal spectra

Jacques Lévy Véhel (1) , Claude Tricot (2)

1 FRACTALES - Fractals, complex models and artificial evolution
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

We introduce two classes of multifractal spectra, called respectively dimension and continuous spectra. Dimension spectra offer an interesting alternative to the classical Hausdorff spectrum: They are much easier to estimate yet still give relevant information about the geometry of the H¨older function. Continuous spectra are a generalization of the large deviation spectrum that allow to obtain partition free results. Both classes of spectra allow to perform efficient multifractal analysis in an experimental framework

Domaines: Probabilités [math.PR]

Jacques Lévy Véhel, Claude Tricot. On various multifractal spectra. Christoph Bandt; Umberto Mosco; Martina Zähle. Fractal Geometry and Stochastics III, 57, Springer, pp.23-42, 2004, Progress in Probability, ⟨10.1007/978-3-0348-7891-3_2⟩. ⟨inria-00559102⟩