On modeling of self-similar random processes in discrete-time

Novel models of stochastic self-similar processes in the discrete-time domain are presented. The results developed are based on the definition of a discrete-time scaling (dilation) operation through a mapping between the discrete and continuous frequencies. It is shown that it is possible to have continuous scaling factors through this operation even though the signal itself is discrete. White noise driven system models of stationary stochastic self-similar random processes are studied. The construction of discrete-time linear scale-invariant (LSI) systems and the LSI system model of discrete-time, non-stationary self-similar random signals are provided. It is shown that a wide class of non-trivial discrete-time self-similar random signals can be constructed through the models presented in the paper.