Geodesic
Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 625-641

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We find the asymptotics for the logarithm of the Laplace transform of the distribution of a compound renewal process as time increases unboundedly. It is assumed that the elements of the governing sequences of the renewal process satisfy Cramér's moment condition. Representations for the deviation rate function of the compound renewal process are found.
Keywords: compound renewal process, large deviations, large deviation principle, Cramér's condition, deviation rate function, Legendre transform, Laplace transform asymptotics. 
@article{TVP_2019_64_4_a0,
     author = {A. A. Borovkov and A. A. Mogul'skii and E. I. Prokopenko},
     title = {Properties of the deviation rate function and the asymptotics for the {Laplace} thansform of the distribution of a compound renewal process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {625--641},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_4_a0/}
}
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A. A. Borovkov; A. A. Mogul'skii; E. I. Prokopenko. Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 4, pp. 625-641. http://geodesic.mathdoc.fr/item/TVP_2019_64_4_a0/