Wavelet construction of Generalized Multifractional processes
Ayache, Antoine ; Jaffard, Stéphane ; Taqqu, Murad S.
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 327-370 / Harvested from Project Euclid
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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 $[0,1]$.
Publié le : 2007-04-14
Classification:  fractional brownian motion,  generalized multifractional brownian motion,  H#x00F6;lder regularity,  60G18,  60G17,  65T16 
@article{1180728896,
     author = {Ayache, Antoine and Jaffard, St\'ephane and Taqqu, Murad S.},
     title = {Wavelet construction of Generalized Multifractional processes},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 327-370},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1180728896}
}

Ayache, Antoine; Jaffard, Stéphane; Taqqu, Murad S. Wavelet construction of Generalized Multifractional processes. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  327-370. http://gdmltest.u-ga.fr/item/1180728896/