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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On probabilities of small deviations for compound {Cox} processes},
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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/

[1] A. A. Mogulskii, “Malye ukloneniya v prostranstve traektorii”, Teoriya veroyatn. i ee primen., 19 (1974), 726–736 | MR

[2] A. A. Borovkov, A. A. Mogulskii, “O veroyatnostyakh malykh uklonenii dlya sluchainykh protsessov”, Trudy Inst. matem. SO AN SSSR, 13, 1989, 147–168 | MR | Zbl

[3] M. Ledoux, “Isoperimetry and Gaussian analysis, Lectures on Probability Theory and Statistics”, Lect. Notes Math., 1648, Springer, Berlin, 1996, 165–294 | MR | Zbl

[4] W. V. Li, Q.-M. Shao, “Gaussian processes: inequalities, small ball probabilities and applications”, Stochastic Processes: Theory and Methods, Handbook of Statistics, 19, eds. C. R. Rao, D. Shanbhag, North-Holland, Amsterdam, 2001, 533–597 | MR | Zbl

[5] M. A. Lifshits, “Asymptotic behavior of small ball probabilities”, Proceedings of the Seventh Vilnius Conference on Probability Theory and Mathematical Statistics, ed. B. Grigelionis, VSP/TEV, Vilnius, 1999, 453–468

[6] P. Embrekhts, K. Klyuppelberg, “Nekotorye aspekty strakhovoi matematiki”, Teoriya veroyatn. i ee primen., 30 (1993), 374–416 | MR

[7] A. I. Martikainen, A. N. Frolov, I. Shtainebakh, “O veroyatnostyakh malykh uklonenii obobschennykh protsessov vosstanovleniya”, Teoriya veroyatn. i ee primen. (to appear)

[8] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1967 | Zbl

[9] I. A. Ibragimov, Yu. V. Linnik, Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965