Lamperti transform and a series decomposition of fractional Brownian motion
Anastassia Baxevani and Krzysztof Podgórski
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2007
ISSN 14039338

Abstract:

The Lamperti transformation of a selfsimilar 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
OrnsteinUhlenbeck processes if H < 1/2, and linear combinations of two
dependent OrnsteinUhlenbeck processes whose two dimensional structure is
Markovian if H > 1/2. 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




Key words:

spectral density, covariance function, stationary Gaussian processes, longrange
dependence
