Geodesic
On probabilities of small deviations for compound Cox processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 163-175

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We derive logarithmic asymtotics for probabilities of small 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 small deviations for compound Cox processes are quite different. 
@article{ZNSL_2006_339_a10,
     author = {A. N. Frolov},
     title = {On probabilities of small deviations for compound {Cox} processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {163--175},
     publisher = {mathdoc},
     volume = {339},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a10/}
}
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A. N. Frolov. On probabilities of small deviations for compound Cox processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 163-175. http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a10/