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Necessary convergence conditions for series ΣαnSn in the case of identically distributed independent random quantities

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Abstract

Necessary (in some cases also sufficient) conditions are obtained for convergence of the series Σa n S n whereS n =Σ n1 ξ k ξk are independent random quantities. The cases in which ξk are symmetrical or identically distributed quantities are investigated in more detail.

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Literature cited

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Authors
  1. V. F. Gaposhkin
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Additional information

Translated from Matematicheskie Zametki, Vol. 20, No. 4, pp. 529–536, October, 1976.

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Gaposhkin, V.F. Necessary convergence conditions for series ΣαnSn in the case of identically distributed independent random quantities. Mathematical Notes of the Academy of Sciences of the USSR 20, 852–857 (1976). https://doi.org/10.1007/BF01098902

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  • DOI: https://doi.org/10.1007/BF01098902

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