An almost sure central limit theorem for self-normalized weighted sums |
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| Authors: | Yong Zhang Xiao-yun Yang |
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| Institution: | 18247. College of Mathematics, Jilin University, Changchun, 130012, China
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| Abstract: | Let X,X 1 ,X 2, … be a sequence of nondegenerate i.i.d. random variables with zero means, which is in the domain of attraction of the normal law. Let {a ni ,1≤i≤n,n≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums. |
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| Keywords: | almost sure central limit theorem self-normalized weighted sums domain of attractio of thenormal law |
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