The limit law of the iterated logarithm for linear processes

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• 作者：Yong Zhang ^{zyong2661@jlu.edu.cn}
• 关键词：60F15 ; 60F05
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：122
• 期：Complete
• 页码：147-151
• 全文大小：369 K
• 卷排序：122

文摘

In this short note, we established the limit law of the iterated logarithm for linear process. Let {ξi,−∞<i<∞}{ξi,−∞<i<∞} be a sequence of independent identically distributed random variables with Eξ1=0Eξ1=0 and Eξ12=1. Define the linear process by Xt=∑j=−∞∞ajξt−j,t≥1 and the partial sum Sn=∑t=1nXt, where {aj,−∞<j<∞}{aj,−∞<j<∞} is a sequence of real numbers with ∑j=−∞∞aj≠0 and ∑j=−∞∞|aj|<∞. Then, we have limn→∞12loglognmax1≤k≤n|Sk|k=|∑j=−∞∞ai|a.s.