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Series Decomposition of fractional Brownian motion and its Lamperti transform

Baxevani, Anastassia LU and Podgorski, Krzysztof LU (2009) In Acta Physica Polonica B, Proceedings Supplement 40(5). p.1395-1435
Abstract
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.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Ornstein-Uhlenbeck process, series representation
in
Acta Physica Polonica B, Proceedings Supplement
volume
40
issue
5
pages
1395 - 1435
publisher
Jagellonian University
external identifiers
  • scopus:67649126584
ISSN
1899-2358
language
English
LU publication?
yes
id
f91e2fed-d9e9-4862-8a7d-26f2cf1687a4 (old id 3049609)
alternative location
http://th-www.if.uj.edu.pl/acta/vol40/pdf/v40p1395.pdf
date added to LUP
2016-04-01 13:44:34
date last changed
2025-01-16 15:59:40
@article{f91e2fed-d9e9-4862-8a7d-26f2cf1687a4,
  abstract     = {{The Lamperti transformation of a self-similar process is a stationary<br/><br>
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 &lt; 1/2, and linear combinations of two dependent Ornstein-Uhlenbeck processes whose two dimensional structure is Markovian if H &gt; 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.<br/><br>
Implications for simulating the fractional Brownian motion are discussed.}},
  author       = {{Baxevani, Anastassia and Podgorski, Krzysztof}},
  issn         = {{1899-2358}},
  keywords     = {{Ornstein-Uhlenbeck process; series representation}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1395--1435}},
  publisher    = {{Jagellonian University}},
  series       = {{Acta Physica Polonica B, Proceedings Supplement}},
  title        = {{Series Decomposition of fractional Brownian motion and its Lamperti transform}},
  url          = {{http://th-www.if.uj.edu.pl/acta/vol40/pdf/v40p1395.pdf}},
  volume       = {{40}},
  year         = {{2009}},
}