Multifractal products of cylindrical pulses
type: Item
instance of: scholarly article
title: Multifractal products of cylindrical pulses
zbMATH Open document ID: 1014.60042
author: Julien Barral
author: Benoît B. Mandelbrot
publication date: 2003-03-18T00:00:00Z
review text: Consider a Poisson process \(S=\{(s_j,\lambda_j)\}\) on \(\mathbb{R}\times(0,1]\) with intensity \(\Lambda(dt d\lambda)=(\delta\lambda^{-2}/2)dt d\lambda\). The cylindrical pulses associated with \(S\) are a denumerable family of functions \(P_j(t)\), such that each \(P_j(t)=W_j\) for \(t\in[s_j-\lambda_j,s_j+\lambda_j]\) and \(P_j(t)=1\) otherwise, where \(W_j\)'s are i.i.d. with \(W\) and independent of \(S\). The multifractal product of the cylindrical pulses is the measure \(\mu\) that appears as the a.s. vague limit as \(\varepsilon\downarrow 0\) of the family of measures \(\mu_\varepsilon\) on \(\mathbb{R}\) with densities proportional to the product of \(P_j(t)\) for \((s_j,\lambda_j)\in S\) with \(\lambda_j\geq\varepsilon\). The authors formulate conditions for non-degeneracy of \(\mu\), existence of the moments and describe the whole multifractal spectrum of \(\mu\).
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1883925
zbMATH Keywords: random measures
zbMATH Keywords: multifractal analysis
zbMATH Keywords: self-similar Poisson point processes
zbMATH Keywords: cylindrical pulses
zbMATH Keywords: measure-valued martingales
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
full work available at URL: s004400200220
OpenAlex ID: W3121850069
DOI: 10.1007/S004400200220
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1883925