Geodesic
On large deviations,~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 672-694

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The Esscher–Cramér approach enables us to get representations of large deviation type even if the Cramér condition fails. Moreover, in the case of the scaled sums of a sequence of independent identically distributed random variables these representations turn out to be slightly different from those which are correct under this rigid condition.
Keywords: generalized Cramér transform, truncated exponential, conditional expectations. 
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     author = {S. V. Zhulenev},
     title = {On large {deviations,~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {672--694},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a2/}
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S. V. Zhulenev. On large deviations,~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 672-694. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a2/