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

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 \([0,1]\).


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