A Curious Converse of Siever's Theorem
Lynch, James
Ann. Probab., Tome 6 (1978) no. 6, p. 169-173 / Harvested from Project Euclid
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A sufficient condition for a sequence of random variables, $T_1, T_2,\cdots$, with cumulant generating functions, $\psi_1, \psi_2,\cdots$, to have a large deviation rate is that $n^{-1}\psi_n(\lambda)\rightarrow \psi(\lambda)$, where $\psi(\lambda)$ satisfies certain regularity conditions. Here it is shown that, when the large deviation rate exists and $T_1, T_2,\cdots$ are properly truncated, it is a necessary condition.
Publié le : 1978-02-14
Classification:  Large deviation rate,  60F10,  62E10,  62E20 
@article{1176995623,
     author = {Lynch, James},
     title = {A Curious Converse of Siever's Theorem},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 169-173},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995623}
}

Lynch, James. A Curious Converse of Siever's Theorem. Ann. Probab., Tome 6 (1978) no. 6, pp.  169-173. http://gdmltest.u-ga.fr/item/1176995623/