A refinement of van der Corput's inequality.
Niu, Da-Wei, Cao, Jian, Qi, Feng (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Niu, Da-Wei, Cao, Jian, Qi, Feng (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Commentationes Mathematicae Universitatis Carolinae
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Let be a sequence of independent random variables such that , , . Let be a sequence od positive integer-valued random variables. Let us put , , , . In this paper we present necessary and sufficient conditions for weak convergence of the sequence , as . The obtained theorems extend the main result of M. Finkelstein and H.G. Tucker (1989).
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Applied Mathematics E-Notes [electronic only]
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Niu, Da-Wei, Cao, Jian, Qi, Feng (2006)
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JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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