Geodesic
Cramer large deviations when the extreme conjugate distribution is heavy-tailed
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 456-475

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The classical large deviations problem is considered under the assumption that the unilateral Cramer condition holds on a bounded interval. We assume that the extreme conjugate distribution is from the domain of attraction of a stable law. A limit is established up to which the asymptotic Cramer–Petrov representation is valid.
Keywords: conjugate distribution, slowly varying function, monotone $\varepsilon$-approximation. 
@article{TVP_1998_43_3_a2,
     author = {A. V. Nagaev},
     title = {Cramer large deviations when the extreme conjugate distribution is heavy-tailed},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {456--475},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a2/}
}
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A. V. Nagaev. Cramer large deviations when the extreme conjugate distribution is heavy-tailed. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 456-475. http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a2/