数学物理学报(英文版)

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STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

林正炎; 李德柜   

  1. 浙江大学数学系, 杭州 310027
  • 收稿日期:2006-01-25 修回日期:1900-01-01 出版日期:2008-01-20 发布日期:2008-01-20
  • 通讯作者: 林正炎
  • 基金资助:
    Supported by NSFC (10571159) and SRFDP (20060335032)

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Lin Zhengyan; Li Degui   

  1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China
  • Received:2006-01-25 Revised:1900-01-01 Online:2008-01-20 Published:2008-01-20
  • Contact: Lin Zhengyan

摘要: Let {Xt,t ≥ 1} be a moving average process defined by
$X_{t}=\sum\limits_{k=0}^{\infty}a_{k}\xi_{t-k}$, where {ak,k ≥ 0} is a sequence of real numbers and {ξt,-∞ < t<∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {ak,k ≥ 0} which entail that {Xt,t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt,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.

关键词: Strong approximation, long memory process, linear process, fractional Brownian motion, the law of the iterated logarithm

Abstract: Let {Xt,t ≥ 1} be a moving average process defined by
$X_{t}=\sum\limits_{k=0}^{\infty}a_{k}\xi_{t-k}$, where {ak,k ≥ 0} is a sequence of real numbers and {ξt,-∞ < t<∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {ak,k ≥ 0} which entail that {Xt,t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt,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

中图分类号: 

  • 60F05