Series decomposition of fractional Brownian motion and its Lamperti transform

Abstract

The Lamperti transformation of a self-similar process is a 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 H1/2. From the representation effective approximations of the process are derived. The corresponding results for the fractional Brownian motion are obtained by applying the inverse Lamperti transformation. Implications for simulating the fractional Brownian motion are discussed.