Lamperti Transform and a Series Decomposition of Fractional Brownian Motion
Författare
Summary, in English
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 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.
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.
Avdelning/ar
Publiceringsår
2007
Språk
Engelska
Publikation/Tidskrift/Serie
Preprints in Mathematical Sciences
Issue
2007:34
Dokumenttyp
Artikel i tidskrift
Förlag
Lund University
Ämne
- Probability Theory and Statistics
Nyckelord
- spectral density
- covariance function
- stationary Gaussian processes
- long-range dependence
Status
Unpublished
ISBN/ISSN/Övrigt
- ISSN: 1403-9338