## Abstract

Let {X-t,t >= 1} be a moving average process defined by X-t = Sigma(infinity)(k=0)a(k)xi(t-k), where {a(k), k >= 0} is a sequence of real numbers and {xi(t), -infinity <t <infinity} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {a(k), k >= 0} which entail that {X-t, t >= 1} is either a long memory process or a linear process, the strong approximation of {X-t, t >= 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

Original language | English |
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Pages (from-to) | 217-224 |

Number of pages | 8 |

Journal | Acta mathematica scientia |

Volume | 28 |

Issue number | 1 |

Publication status | Published - Jan 2008 |

## Keywords

- fractional Brownian motion
- strong approximation
- the law of the iterated logarithm
- RANDOM-VARIABLES
- linear process
- long memory process