Wavelet-based synthesis of the Rosenblatt process

Based on a wavelet-type expansion of the Rosenblatt process, we introduce and examine two different practical ways to simulate the Rosenblatt process. The synthesis procedures proposed here are obtained by either truncating the series of the approximation term or using the approximation coefficients in the wavelet-type expansion of the Rosenblatt process. Both benefit from the low computational cost usually associated with the discrete wavelet transform. We show that the number of zero moments of a related orthogonal multiresolution analysis plays an important role. We study in detail the wavelet-based simulation in terms of uniform convergence. We also discuss at length the importance of the choices of the initial and final resolutions, the specific case of the simulation on the integer grid as well as the usefulness of the wavelet-based simulation. Matlab routines implementing these synthesis procedures as well as their analysis are available upon request.