PreprintOn large deviations of sums of independent random variablesZhishui Hu, Valentin V. Petrov, John RobinsonAbstractExtensions of some limit theorems are proved for tail probabilities of sums of independent identically distributed random variables satisfying the onesided or twosided Cramér's condition. The large deviation xregion 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 obtainedKeywords: Limit theorems; sums of independent random variables; large deviation; Cramér's condition; asymptotic expansions. AMS Subject Classification: Primary 60F10; Secondary 60G50, 62E20.
