Open Access
April, 2007 Wavelet construction of Generalized Multifractional processes
Antoine Ayache, Stéphane Jaffard, Murad S. Taqqu
Rev. Mat. Iberoamericana 23(1): 327-370 (April, 2007).


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 H#x00F6;lder exponent function possible, namely, a random H#x00F6;lder exponent which is a function of time and which can be expressed in the strong sense (almost surely for all $t$), as a $\liminf$ of an arbitrary sequence of continuous processes with values in $[0,1]$.


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Antoine Ayache. Stéphane Jaffard. Murad S. Taqqu. "Wavelet construction of Generalized Multifractional processes." Rev. Mat. Iberoamericana 23 (1) 327 - 370, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1123.60022
MathSciNet: MR2351137

Primary: 60G17 , 60G18
Secondary: 65T16

Keywords: fractional Brownian motion , generalized multifractional brownian motion , H#x00F6;lder regularity

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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