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Series Decomposition of fractional Brownian motion and its Lamperti transform

Publiceringsår: 2009
Språk: Engelska
Sidor: 1395-1435
Publikation/Tidskrift/Serie: Acta Physica Polonica B
Volym: 40
Nummer: 5
Dokumenttyp: Artikel
Förlag: Jagiellonian University, Cracow, Poland


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.



  • Probability Theory and Statistics
  • Ornstein-Uhlenbeck process
  • series representation


  • ISSN: 1899-2358

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