Lamperti Transform and a Series Decomposition of Fractional Brownian Motion
The Lamperti transformation of a self-similar process is a strictly stationary process. In particular, the fractional Brownian motion transforms to the second order stationary Gaussian process. This process is represented as a series of independent processes. The terms of this series are Ornstein-Uhlenbeck processes if $H<1/2$, and linear combinations of two dependent Ornstein-Uhlenbeck processes
