Lamperti transform of fractional Brownian motion
Artikel i vetenskaplig tidskrift, 2009

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 $H<1/2$, and linear combinations of two dependent Ornstein-Uhlenbeck 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.

05.10.Gg

87.10.Mn.

PACS numbers: 02.50.Ey

Författare

Anastassia Baxevani

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Krzysztof Podgórski

Acta Physica Polonica B

Vol. 40 1395-1435

Ämneskategorier

Sannolikhetsteori och statistik