Moments, continuity, and multifractal analysis of Mandelbrot martingales
type: Item
instance of: scholarly article
title: Moments, continuity, and multifractal analysis of Mandelbrot martingales
zbMATH Open document ID: 0936.60045
author: Julien Barral
publication date: 2000-05-09T00:00:00Z
review text: Let Mandelbrot measure be a statistically self-similar measure \(\mu\) on the boundary of a \(c\)-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. The author takes particular interest in the random variable \(Y=\|\mu\|\). He studies the existence of finite moments of negative orders for \(Y\), conditionally to \(Y>0\), and the continuity properties of \(Y\) with respect to the weights. These results on moments make it possible to study, with probability one, the existence of local Hölder exponent for \(\mu\), almost everywhere with respect to another Mandelbrot measure, as well as to perform the multifractal analysis of \(\mu\), under hypotheses that are weaker than those usually assumed.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 1300445
zbMATH Keywords: multifractal analysis
zbMATH Keywords: Mandelbrot martingale
zbMATH Keywords: local Hölder exponent
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: s004400050217
OpenAlex ID: W2049628118
DOI: 10.1007/S004400050217
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1300445