A class of second-order stationary self-similar processes for 1/f phenomena

We propose a class of statistically self-similar processes and outline an alternative mathematical framework for the modeling and analysis of 1/f phenomena. The foundation of the proposed class is based on the extensions of the basic concepts of classical time series analysis, in particular, on the notion of stationarity. We consider a class of stochastic processes whose second-order structure is invariant with respect to time scales, i.e., E[X(t)X(/spl lambda/t)]=t/sup 2H//spl lambda//sup H/R(/spl lambda/), t>0 for some -x