Wavelet-Based Synthesis of a Multifractional Process

The multifractional process is introduced as a natural extension of traditional monofractional process. The selling point of multifractional process is that its Hölder regularity is allowed to vary from point to point, such that makes it a promising model for those stochastic processes whose regularity evolves in time. A new wavelet-based algorithm to synthesize a realization of multifractional process is proposed, and the validity is verified by numerical experiments and real-world data.