Abstract
One finds necessary and sufficient conditions for the convergence of series of weighted probabilities of large deviations for sums of independent random variables with multidimensional indices. These conditions are expressed in terms of the initial distribution.
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Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 114–131, 1986.
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Gafurov, M.U., Kholmuradov, M.K. Convergence of series of probabilities of large deviations for sums of random variables with multidimensional indices. J Math Sci 38, 2230–2239 (1987). https://doi.org/10.1007/BF01093824
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DOI: https://doi.org/10.1007/BF01093824