STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Lin Zhengyan; Li Degui

doi:10.1016/S0252-9602(08)60023-5

Acta mathematica scientia, Series B >

2008 , Vol. 28 >Issue 1: 217 - 224

DOI: https://doi.org/10.1016/S0252-9602(08)60023-5

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STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Lin Zhengyan ,
Li Degui

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Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received date: 2006-01-25

Revised date: 1900-01-01

Online published: 2008-01-20

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Abstract

Let {X_t,t ≥ 1} be a moving average process defined by
$X_{t}=\sum\limits_{k=0}^{\infty}a_{k}\xi_{t-k}$, where {a_k,k ≥ 0} is a sequence of real numbers and {ξ_t,-∞ < t<∞} 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.

Key words： Strong approximation; long memory process; linear process; fractional Brownian motion; the law of the iterated logarithm

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Lin Zhengyan , Li Degui . STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS[J]. Acta mathematica scientia, Series B, 2008 , 28(1) : 217 -224 . DOI: 10.1016/S0252-9602(08)60023-5

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