Series Decomposition of fractional Brownian motion and its Lamperti transform
Author
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.
Department/s
Publishing year
2009
Language
English
Pages
1395-1435
Publication/Series
Acta Physica Polonica B, Proceedings Supplement
Volume
40
Issue
5
Links
Document type
Journal article
Publisher
Jagellonian University, Cracow, Poland
Topic
- Probability Theory and Statistics
Keywords
- Ornstein-Uhlenbeck process
- series representation
Status
Published
ISBN/ISSN/Other
- ISSN: 1899-2358