Multiperiodic multifractal martingale measures.
type: Item
instance of: scholarly article
title: Multiperiodic multifractal martingale measures.
zbMATH Open document ID: 1047.28003
DOI: 10.1016/S0021-7824(03)00035-7
author: M.-O. Coppens
author: Julien Barral
author: Benoît B. Mandelbrot
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2004-01-26T00:00:00Z
review text: A nonnegative 1-periodic multifractal measure on the reals is obtained as infinite random product of harmonics of a 1-periodic function. Such infinite products are statistically self-affine, they generalize Riesz products and being martingale structures, they converge. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points. The paper employs both large deviation estimates and the thermodynamic formalism for random transformations.
reviewed by: Yuri Kifer
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 2032769
zbMATH Keywords: multifractal measure
zbMATH Keywords: martingale
zbMATH Keywords: Riesz products
zbMATH Keywords: random transformations
zbMATH Keywords: random measure
zbMATH Keywords: thermodynamic formalism
MaRDI profile type: Publication
cites work: Continuity of the multifractal spectrum of a random statistically self-similar measure
cites work: Comparing multifractal formalisms: the neighboring boxes condition
cites work: Multifractal products of cylindrical pulses
cites work: Q5515914
cites work: On the multifractal analysis of measures
cites work: Q4495249
cites work: Large deviations for a general class of random vectors
cites work: Techniques in fractal geometry
cites work: An approximate formula for the dimension of certain Riesz products
cites work: Q4865381
cites work: Multifractal analysis of infinite products
cites work: Asymptotic behavior of multiperiodic functions \(G(x)=\prod_{n=1}^\infty g(x/2^n)\)
cites work: Positive martingales and random measures
cites work: Sur certaines martingales de Benoit Mandelbrot
cites work: Large deviation for weak Gibbs measures and multifractal spectra
cites work: Q4867126
cites work: Q5288793
cites work: Q4861727
cites work: Q5635152
cites work: Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
cites work: Q4226831
cites work: A multifractal formalism
cites work: A cascade decomposition theory with applications to Markov and exchangeable cascades
cites work: Weak Gibbs measures for certain non-hyperbolic systems
cites work: Q3254471
full work available at URL: s0021-7824(03)00035-7
OpenAlex ID: W1974815410
description: scientific article; zbMATH DE number 2032769