Abstract
We consider sums of independent random variables within the scheme of series. We focus on the case where every summand has a zero mean and finite variance and sums have unit variances. We obtain a criterion of stochastic compactness (defined by W. Feller) for sequences of distributions of such sums. The condition of uniform asymptotic negligibility of summands is not supposed.
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∗ The work was supported by the RFBR grant 16-01-00258 and partially supported by the Government of the Russian Federation (grant 074-U01), by Ministry of Science and Education of the Russian Federation (GOSZADANIE 2014/190, Project Nos. 14.Z50.31.0031 and 1.754.2014/K), and by grant MK-5001.2015.1 of the President of the Russian Federation.
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Khartov, A. Stochastic compactness of distributions of sums of independent random variables with finite variances∗ . Lith Math J 57, 196–203 (2017). https://doi.org/10.1007/s10986-017-9353-4
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DOI: https://doi.org/10.1007/s10986-017-9353-4