Wavelet construction of generalized multifractional processes (Q997821)

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 \([0,1]\).