On the continuous wavelet transform of second-order random processes
Stamatis Cambanis, Christian Houdré · IEEE Transactions on Information Theory · 1995
Some second-order properties of random processes such as periodic correlation, stationarity, harmonizability, self-similarity, are characterized via corresponding properties of their wavelet transform: any one of these properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. These results are then specialized to fractional Brownian motion and other self-similar processes.>