On large deviations of sums of independent random variables

Zhishui Hu, Valentin V. Petrov, John Robinson


Extensions of some limit theorems are proved for tail probabilities of sums of independent identically distributed random variables satisfying the one-sided or two-sided Cramér's condition. The large deviation x-region under consideration is broader than in the classical Cramér's theorem, and the estimate of the remainder is uniform with respect to x. The corresponding asymptotic expansion with arbitrarily many summands is also obtained

Keywords: Limit theorems; sums of independent random variables; large deviation; Cramér's condition; asymptotic expansions.

AMS Subject Classification: Primary 60F10; Secondary 60G50, 62E20.

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Wednesday, April 26, 2006