Du är här

Lamperti Transform and a Series Decomposition of Fractional Brownian Motion

Författare:
Publiceringsår: 2007
Språk: Engelska
Sidor: 40
Publikation/Tidskrift/Serie: Preprints in Mathematical Sciences
Nummer: 2007:34
Dokumenttyp: Opublicerad artikel
Förlag: Lund University

Sammanfattning

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.

Disputation

Nyckelord

  • Mathematics and Statistics
  • spectral density
  • covariance function
  • stationary Gaussian processes
  • long-range dependence

Övriga

Submitted
  • ISSN: 1403-9338

Box 117, 221 00 LUND
Telefon 046-222 00 00 (växel)
Telefax 046-222 47 20
lu [at] lu [dot] se

 

Fakturaadress: Box 188, 221 00 LUND
Organisationsnummer: 202100-3211
Om webbplatsen