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An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables |
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| Authors: | Yong Zhang Xiao-Yun Yang |
| Affiliation: | College of Mathematics, Jilin University, Changchun 130012, PR China |
| Abstract: | Let X,X1,X2,… be a sequence of independent and identically distributed positive random variables with EX=μ>0. In this paper we show that the almost sure central limit theorem for self-normalized products of sums holds only under the assumptions that X belongs to the domain of attraction of the normal law. |
| Keywords: | Almost sure central limit theorem Self-normalized Products of sums Domain of attraction of the normal law |
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