Abstract
A combinatorial inequality is derived. This inequality is applied to obtain new estimates for probabilities of large deviations of normalized and self-normalized sums of independent and dependent positive random values. As a consequence, an estimate from above is derived for the strong law of large numbers. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 77–87.
This research was supported in part by the Ministry of Education of Russia, grant E00-1.0-45, and by the Russian Foundation for Basic Research, grant 02-01-01099a.
Translated by V. A. Egorov.
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Egorov, V.A. Estimation of distribution tails for normalized and self-normalized sums. J Math Sci 127, 1717–1722 (2005). https://doi.org/10.1007/s10958-005-0132-0
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DOI: https://doi.org/10.1007/s10958-005-0132-0