Random Wavelet Series Based on a Tree-Indexed Markov Chain |
| |
Authors: | Arnaud Durand |
| |
Institution: | (1) Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris XII, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France;(2) Present address: Applied and Computational Mathematics – MC 217-50, California Institute of Technology, Pasadena, CA 91125, USA |
| |
Abstract: | We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show that almost every sample path displays an oscillating singularity at almost every point and that the points at which a sample path has at most a given Hölder exponent form a set with large intersection. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|