Revista Matemática Iberoamericana


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Volume 23, Issue 1, 2007, pp. 327–370
DOI: 10.4171/RMI/497

Published online: 2007-04-30

Wavelet construction of Generalized Multifractional processes

Antoine Ayache[1], Stéphane Jaffard[2] and Murad S. Taqqu[3]

(1) Université Lille 1, Villeneuve d'Asq, France
(2) Université Paris Est, Créteil, France
(3) Boston University, USA

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 $[0,1]$.

Keywords: Fractional brownian motion, generalized multifractional brownian motion, Hölder regularity

Ayache Antoine, Jaffard Stéphane, Taqqu Murad: Wavelet construction of Generalized Multifractional processes. Rev. Mat. Iberoamericana 23 (2007), 327-370. doi: 10.4171/RMI/497