Wavelet construction of generalized multifractional processes. (English) Zbl 1123.60022

Ayache, Antoine; Jaffard, Stéphane; Taqqu, Murad S.

Rev. Mat. Iberoam. 23, No. 1, 327-370 (2007).

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 \([0,1]\).

MSC:

60G18	Self-similar stochastic processes
60G17	Sample path properties
60G15	Gaussian processes

Keywords:

fractional Brownian motion; generalized multifractional Brownian motion; Hölder regularity

References:

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