Necessity of the Cramer, Linnik, and Statulevičius conditions for large-deviation probabilities
The Cramer, Linnik, and Statulevičius conditions, well-known in the field of the limit theorems for large deviations, are shown to be necessary in theorems on large-deviation probabilities formulated in the respective way. The Statulevičius condition is shown to be a generalization of the Cramer and Linnik conditions. See also the author [in: Rings and modules. Limit theorems of probability theory 1, 131-134 (1986); J. Math. Sci., New York 93, 255-258 (1999); translation from Zap. Nauchn. Semin. POMI 228, 9-15 (1996; Zbl 0929.60018); and Lith. Math. J. 39, 231-239 (1999); translation from Liet. Mat. Rink. 39, 293-303 (1999; Zbl 0966.60021)].
scientific article; zbMATH DE number 1759197