Abstract
Consider a sequence of i.i.d. positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1, 2]. A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan. In a sense, our results reach the optimal form.
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Project supported by the National Natural Science Foundation of China (No. 11061012) and the Natural Science Foundation of Guangxi Province (No. 2012GXNSFAA053010).
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Wu, Q. An improved result in almost sure central limit theory for products of partial sums with stable distribution. Chin. Ann. Math. Ser. B 33, 919–930 (2012). https://doi.org/10.1007/s11401-012-0742-z
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DOI: https://doi.org/10.1007/s11401-012-0742-z