Wavelet construction of Generalized Multifractional processes
Antoine Ayache, Stéphane Jaffard, Murad S. Taqqu · Revista Matemática Iberoamericana · 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] .