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 Zap. Nauchn. Sem. POMI, 2008, Volume 361, Pages 167–181 (Mi znsl2188)

On asymptotic behaviour of probabilities of large deviations for compound Cox processes

A. N. Frolov

Saint-Petersburg State University

Abstract: 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.

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English version:
Journal of Mathematical Sciences (New York), 2009, 159:3, 376–383

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UDC: 519.2

Citation: A. N. Frolov, “On asymptotic behaviour of probabilities of large deviations for compound Cox processes”, Probability and statistics. Part 13, Zap. Nauchn. Sem. POMI, 361, POMI, St. Petersburg, 2008, 167–181; J. Math. Sci. (N. Y.), 159:3 (2009), 376–383

Citation in format AMSBIB
\Bibitem{Fro08} \by A.~N.~Frolov \paper On asymptotic behaviour of probabilities of large deviations for compound Cox processes \inbook Probability and statistics. Part~13 \serial Zap. Nauchn. Sem. POMI \yr 2008 \vol 361 \pages 167--181 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl2188} \zmath{https://zbmath.org/?q=an:1185.60023} \transl \jour J. Math. Sci. (N. Y.) \yr 2009 \vol 159 \issue 3 \pages 376--383 \crossref{https://doi.org/10.1007/s10958-009-9450-y} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349148584} 

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This publication is cited in the following articles:
1. A. N. Frolov, “On asymptotic behaviour of probabilities of large and moderate deviations for some iterated stochastic processes”, J. Math. Sci. (N. Y.), 167:4 (2010), 566–573
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