Geodesic
From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 489-508

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We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a random variable whose MGF is finite only on part of the real line. We relate the right tail behavior of the cumulative distribution function of such a random variable to the behavior of its MGF near the critical moment. We apply our results to an arbitrary superposition of a CIR process and the time-integral of this process.
Keywords: regular variation, Tauberian theorems, moment generating function, tail asymptotic, CIR process. 
@article{TVP_2016_61_3_a3,
     author = {S. M. Aly},
     title = {From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {489--508},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a3/}
}
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S. M. Aly. From moment explosion to the asymptotic behavior of the cumulative distribution for a random variable. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 489-508. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a3/