Abstract
Consider a sequence of i.i.d. positive random variables. An universal result in almost sure limit theorem for products of sums of partial sums is established. We will show that the almost sure limit theorem holds under a fairly general condition on the weight d k = k −1 exp(lnβ k), 0 ≤ β < 1. And in a sense, our results have reached the optimal form.
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Supported by the National Natural Science Foundation of China (11061012), Project Supported by Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011]47), and the Guangxi Natural Science Foundation of China (2012GXNSFAA053010).
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Wu, Qy. Almost sure central limit theory for products of sums of partial sums. Appl. Math. J. Chin. Univ. 27, 169–180 (2012). https://doi.org/10.1007/s11766-012-2823-x
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DOI: https://doi.org/10.1007/s11766-012-2823-x