Lamperti Transform and a Series Decomposition of Fractional Brownian Motion
(2007) In Preprints in Mathematical Sciences- Abstract
- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/938292
- author
- Baxevani, Anastassia and Podgorski, Krzysztof LU
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- unpublished
- subject
- keywords
- spectral density, covariance function, stationary Gaussian processes, long-range dependence
- in
- Preprints in Mathematical Sciences
- issue
- 2007:34
- pages
- 40 pages
- publisher
- Lund University
- ISSN
- 1403-9338
- language
- English
- LU publication?
- yes
- id
- 6959686f-5e98-43e3-8db8-21c1b2ed3bf7 (old id 938292)
- date added to LUP
- 2016-04-01 16:58:33
- date last changed
- 2018-11-21 20:45:37
@article{6959686f-5e98-43e3-8db8-21c1b2ed3bf7,
abstract = {{The Lamperti transformation of a self-similar process is a strictly stationary process.<br/><br>
In particular, the fractional Brownian motion transforms to the second order stationary Gaussian process.<br/><br>
This process is represented as a series of independent processes.<br/><br>
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 $H>1/2$.<br/><br>
From the representation effective approximations of the process are derived.<br/><br>
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 = {{1403-9338}},
keywords = {{spectral density; covariance function; stationary Gaussian processes; long-range dependence}},
language = {{eng}},
number = {{2007:34}},
publisher = {{Lund University}},
series = {{Preprints in Mathematical Sciences}},
title = {{Lamperti Transform and a Series Decomposition of Fractional Brownian Motion}},
year = {{2007}},
}