Abstract
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
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References
Arnold B C and Villaseñr J A, The asymptotic distribution of sums of records, Extremes 1(3) (1998) 351–363
Berkes I and Csáki E, A universal result in almost sure central limit theory, Stoch. Proc. Appl. 94 (2001) 105–134
Brosamler G, An almost everywhere central limit theorem, Math. Proc. Cambridge Philos. Soc. 104 (1988) 561–574
Gonchigdanzan K and Rempała G A, A note on the almost sure limit theorem for the product of partial sums, Appl. Math. Lett. 19 (2006) 191–196
Lacey M and Philipp W A, note on the almost everywhere central limit theorem, Statist. Probab. Lett. 9 (1990) 201–205
Lu X W and Qi Y C, A note on asymptotic distribution of products of sums, Statist. Probab. Lett. 68(4) (2004) 407–413
Qi Y C, Limit distributions for products of sums, Statist. Probab. Lett. 62(1) (2003) 93–100
Rempała G A and Wesołowski J, Asymptotics for products of sums and U-statistics, Electron. Comm. Probab. 7 (2002) 47–54
Schatte P, On strong versions of the central limit theorem, Math. Nachr. 137 (1988) 249–256
Zhang L X and Huang W, A note on the invariance principle of the product of sums of random variables, arXiv:math.PR/0610515 v1, 17 Oct. 2006
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Yu, M. Central limit theorem and almost sure central limit theorem for the product of some partial sums. Proc Math Sci 118, 289–294 (2008). https://doi.org/10.1007/s12044-008-0021-9
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DOI: https://doi.org/10.1007/s12044-008-0021-9