Geodesic
On asymptotic behaviour of probabilities of large deviations for compound Cox processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 167-181

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We derive logarithmic asymptotics for probabilities of large deviations for compound Cox processes. We show that under appropriate conditions, these asymptotics are the same as those for sums of independent random variables and processes with independent increments. When these conditions do not hold, the asymptotics of large deviations probabilities for compound Cox processes are quite different. Bibl. – 5 titles. 
@article{ZNSL_2008_361_a11,
     author = {A. N. Frolov},
     title = {On asymptotic behaviour of probabilities of large deviations for compound {Cox} processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--181},
     publisher = {mathdoc},
     volume = {361},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a11/}
}
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A. N. Frolov. On asymptotic behaviour of probabilities of large deviations for compound Cox processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 167-181. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a11/