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Characteristic Functions and Compactness of Distributions of Sums of Independent Random Variables

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The sequences of distributions of centered sums of independent random variables are considered within the framework of the series scheme, without assuming the classical conditions for uniform asymptotic smallness and uniform limit constancy. Necessary and sufficient conditions are obtained for relative and stochastic compactness of such sequences in terms of the characteristic functions of summable random variables and with using their τ-centers.

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Authors and Affiliations

  1. St.Petersburg State University; St.Petersburg National Research University of Information Technologies, Mechanics and Optics, St.-Petersburg, Russia

    A. A. Khartov

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  1. A. A. Khartov
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Correspondence to A. A. Khartov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 454, 2017, pp. 292–308.

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Khartov, A.A. Characteristic Functions and Compactness of Distributions of Sums of Independent Random Variables. J Math Sci 229, 792–802 (2018). https://doi.org/10.1007/s10958-018-3719-y

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  • DOI: https://doi.org/10.1007/s10958-018-3719-y

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