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Lamperti Transform and a Series Decomposition of Fractional Brownian Motion

Baxevani, Anastassia and Podgorski, Krzysztof LU (2007) In Preprints in Mathematical Sciences1999-01-01+01:00
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)
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
spectral density, covariance function, stationary Gaussian processes, long-range dependence
in
Preprints in Mathematical Sciences1999-01-01+01:00
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
2008-01-24 12:11:11
date last changed
2016-04-16 05:09:38
@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 $H&lt;1/2$, and linear combinations of two dependent Ornstein-Uhlenbeck processes whose two dimensional structure is Markovian if $H&gt;1/2$.<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},
  keyword      = {spectral density,covariance function,stationary Gaussian processes,long-range dependence},
  language     = {eng},
  number       = {2007:34},
  pages        = {40},
  publisher    = {Lund University},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Lamperti Transform and a Series Decomposition of Fractional Brownian Motion},
  year         = {2007},
}