Alternative micropulses and fractional Brownian motion
type: Item
instance of: scholarly article
title: Alternative micropulses and fractional Brownian motion
zbMATH Open document ID: 0879.60076
DOI: 10.1016/S0304-4149(96)00089-0
published in: Stochastic Processes and their Applications
publication date: 1997-12-10T00:00:00Z
review text: The generation of fractional Brownian motion (FBM) as a fractal sum of micropulses is considered [cf. \textit{B. B. Mandelbrot} and \textit{J. W. Van Ness}, SIAM Rev. 10, 422-437 (1968; Zbl 0179.47801)]). In an earlier paper of the authors [Stochastic Process Appl. 60, 1-8 (1995; Zbl 0846.60055)], rectangular pulses leading to negatively correlated (the self-affinity exponent \(H<1/2\)) FMB's have been examined. More general pulse shapes are treated here starting with conical and semiconical pulses and ending with Lévy staircase, Cantor pyramid and multifractal staircase. The location of the pulse, its width and height are random, the transformation of a pulse proceeds by letting the tangent of the base angle go to zero. It is shown that only pulses without jumps at their starting and ending points generate positively correlated and ordinary Brown motion (\(H\geq 1/2\)).
reviewed by: Ivan Saxl
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1095924
zbMATH Keywords: fractal sums of micropulses
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: self-affinity
author: Renata Cioczek-Georges
author: Benoît B. Mandelbrot
MaRDI profile type: Publication
cites work: A class of micropulses and antipersistent fractional Brownian motion
cites work: Stable fractal sums of pulses: The cylindrical case
cites work: Q4209136
cites work: Q4740120
cites work: Q4850564
cites work: Fractional Brownian Motions, Fractional Noises and Applications
cites work: Q3771297
full work available at URL: s0304-4149(96)00089-0
OpenAlex ID: W2042963681
Wikidata QID: Q127205804
description: scientific article; zbMATH DE number 1095924