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

We introduce a class of stochastic processes whose correlation function obeys a structure of the form, E[X(t)X(λt)]=t^2H λ^HR(λ), λ,t>0. We refer to these processes as second order self-similar processes. This class of processes include fractional Brownian motion as a special case. We define a concept of autocorrelation and develop a spectral analysis framework via generalized Mellin transform for the proposed class. Additionally, we establish a relationship between the proposed self-similar processes and generalized linear scale invariant system theory. We give specific models and demonstrate their ability to model 1/f phenomena