Higher and lower-order properties of the wavelet decomposition of self-similar processes

Abstract

Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit "1/f" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.