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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive
Teor. Veroyatnost. i Primenen., 2001 Volume 46, Issue 4, Pages 785–792 (Mi tvp3825)
This article is cited in 8 papers

Short Communications

Lower Bounds for Probabilities of Large Deviations of Sums of Independent Random Variables

S. V. Nagaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We derive lower bounds for probabilities of large deviations of sums of independent random variables in terms of tail probabilities for the number of successes in nonhomogeneous Bernoulli trials. These bounds are convenient if the Lyapunov ratio is great, and also in the case of bounded summands.

Keywords: binomial distribution, large deviations, Poisson distribution, Lyapunov ratio, Bernoulli trials, Cramer theorem.

Received: 08.02.1999

DOI: 10.4213/tvp3825


 English version: Theory of Probability and its Applications, 2002, 46:4, 728–735

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