Geodesic
Lower Bounds for Probabilities of Large Deviations of Sums of Independent Random Variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 785-792

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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.
Mots-clés : binomial distribution, Poisson distribution
Keywords: large deviations, Lyapunov ratio, Bernoulli trials, Cramer theorem. 
@article{TVP_2001_46_4_a10,
     author = {S. V. Nagaev},
     title = {Lower {Bounds} for {Probabilities} of {Large} {Deviations} of {Sums} of {Independent} {Random} {Variables}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {785--792},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a10/}
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S. V. Nagaev. Lower Bounds for Probabilities of Large Deviations of Sums of Independent Random Variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 785-792. http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a10/