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Zap. Nauchn. Sem. POMI, 2003, Volume 298, Pages 280–303 (Mi znsl1209)  

This article is cited in 5 scientific papers (total in 5 papers)

Small ball probability for centered Poisson process of high intensity

E. Yu. Shmileva

Saint-Petersburg State University

Abstract: We study the limiting behavior of the probability with which the path of a centered Poisson process of high intensity gets into a small ball with a receding center. The results of this paper are restricted to the simplest case where the variation of the shift function (center of the ball) is finite. The estimates are obtained under the optimal conditions for the intensity of the process.

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English version:
Journal of Mathematical Sciences (New York), 2005, 128:1, 2656–2668

Bibliographic databases:

UDC: 519.2
Received: 29.09.2003

Citation: E. Yu. Shmileva, “Small ball probability for centered Poisson process of high intensity”, Probability and statistics. Part 6, Zap. Nauchn. Sem. POMI, 298, POMI, St. Petersburg, 2003, 280–303; J. Math. Sci. (N. Y.), 128:1 (2005), 2656–2668

Citation in format AMSBIB
\Bibitem{Shm03}
\by E.~Yu.~Shmileva
\paper Small ball probability for centered Poisson process of high intensity
\inbook Probability and statistics. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 298
\pages 280--303
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1209}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2038877}
\zmath{https://zbmath.org/?q=an:1074.60059}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 1
\pages 2656--2668
\crossref{https://doi.org/10.1007/s10958-005-0213-0}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tomas Simon, “Malye ukloneniya negaussovskikh protsessov”, Theory Stoch. Process., 13(29):2 (2007), 272–280  mathnet
    2. Varron D., “Some new almost sure results on the functional increments of the uniform empirical process”, Stochastic Process Appl, 121:2 (2011), 337–356  crossref  mathscinet  zmath  isi  elib  scopus
    3. Buchmann B., Maller R., “The small-time Chung-Wichura law for Levy processes with non-vanishing Brownian component”, Probab Theory Related Fields, 149:1–2 (2011), 303–330  crossref  mathscinet  zmath  isi  elib  scopus
    4. Varron D., “Functional limit laws for local empirical processes in a spatial setting”, Stochastics, 88:3 (2016), 373–395  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236  crossref  isi  scopus
  • Записки научных семинаров ПОМИ
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