Series Decomposition of fractional Brownian motion and its Lamperti transform
Författare
Summary, in English
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.
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.
Avdelning/ar
Publiceringsår
2009
Språk
Engelska
Sidor
1395-1435
Publikation/Tidskrift/Serie
Acta Physica Polonica B, Proceedings Supplement
Volym
40
Issue
5
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Jagellonian University, Cracow, Poland
Ämne
- Probability Theory and Statistics
Nyckelord
- Ornstein-Uhlenbeck process
- series representation
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1899-2358