Wavelet construction of generalized multifractional processes
type: Item
instance of: scholarly article
title: Wavelet construction of generalized multifractional processes
zbMATH Open document ID: 1123.60022
DOI: 10.4171/RMI/497
author: Antoine Ayache
author: Stéphane Jaffard
author: Murad S. Taqqu
published in: Revista Matemática Iberoamericana
publication date: 2007-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/43597
review text: Summary: We construct generalized multifractional processes with random exponent (GMPREs). These processes, defined through a wavelet representation, are obtained by replacing the Hurst parameter of fractional Brownian motion by a sequence of continuous random processes. We show that these GMPREs can have the most general pointwise Hölder exponent function possible, namely, a random Hölder exponent which is a function of time and which can be expressed in the strong sense (almost surely for all \(t)\), as a lim inf of an arbitrary sequence of continuous processes with values in \([0,1]\).
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 5177716
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: generalized multifractional Brownian motion
zbMATH Keywords: Hölder regularity
MaRDI profile type: Publication
cites work: Characterization of pointwise Hölder regularity
OpenAlex ID: W2015187233
description: scientific article; zbMATH DE number 5177716