Series Decomposition of fractional Brownian motion and its Lamperti transform

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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.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Ornstein-Uhlenbeck process, series representation
Original languageEnglish
Pages (from-to)1395-1435
JournalActa Physica Polonica. B, Proceedings Supplement
Volume40
Issue number5
Publication statusPublished - 2009
Publication categoryResearch
Peer-reviewedYes