Abstract
Necessary and sufficient conditions are presented for the weak convergence of random sums of independent identically distributed random variables in the double array scheme. As corollaries, two criteria of the normal convergence of random sums are given.
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Supported by the Russian Foundation for Fundamental Research (grant No. 96-011-01919).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.
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Korolev, V.Y., Kruglov, V.M. A criterion of convergence of nonrandomly centered random sums of independent identically distributed random variables. J Math Sci 89, 1495–1506 (1998). https://doi.org/10.1007/BF02362284
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DOI: https://doi.org/10.1007/BF02362284