Strong approximation for moving average processes under dependence assumptions

[No Value] Lin Zhengyan, [No Value] Li Degui, Degui Li

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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 languageEnglish
Pages (from-to)217-224
Number of pages8
JournalActa mathematica scientia
Issue number1
Publication statusPublished - Jan 2008


  • fractional Brownian motion
  • strong approximation
  • the law of the iterated logarithm
  • linear process
  • long memory process

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