## 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.

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.

Original language | English |
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Pages (from-to) | 1395-1435 |

Journal | Acta Physica Polonica B, Proceedings Supplement |

Volume | 40 |

Issue number | 5 |

Publication status | Published - 2009 |

## Subject classification (UKÄ)

- Probability Theory and Statistics

## Free keywords

- Ornstein-Uhlenbeck process
- series representation