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.