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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 278, Pages 63–85 (Mi znsl1435)  
This article is cited in 7 scientific papers (total in 7 papers)

Probabilities of hitting of shifted small balls by the centered Poisson process

P. Deheuvelsa, M. A. Lifshitsb

a Université Pierre & Marie Curie, Paris VI
b Saint-Petersburg State University
Full-text PDF (284 kB) Citations (7)
Abstract: We investigate the probabilities of hitting shifted small balls by sample paths of centered Poisson process and find the exact range of parameters where Wiener approximation of those probabilities is valid. Towards this aim, we introduce the Skorokhod density technique which, for the Poisson process, plays a role similar to that of the Cameron–Martin formula in construction of associated laws for Gaussian measure.
Received: 24.11.2000
English version:
Journal of Mathematical Sciences, 2003, Volume 18, Issue 6, Pages 5541–5554
DOI: https://doi.org/10.1023/A:1026182304492
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: P. Deheuvels, M. A. Lifshits, “Probabilities of hitting of shifted small balls by the centered Poisson process”, Probability and statistics. Part 4, Zap. Nauchn. Sem. POMI, 278, POMI, St. Petersburg, 2001, 63–85; J. Math. Sci., 18:6 (2003), 5541–5554
Citation in format AMSBIB
\Bibitem{DehLif01}
\by P.~Deheuvels, M.~A.~Lifshits
\paper Probabilities of hitting of shifted small balls by the centered Poisson process
\inbook Probability and statistics. Part~4
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 278
\pages 63--85
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1435}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1874390}
\zmath{https://zbmath.org/?q=an:1077.60034}
\transl
\jour J. Math. Sci.
\yr 2003
\vol 18
\issue 6
\pages 5541--5554
\crossref{https://doi.org/10.1023/A:1026182304492}
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  • https://www.mathnet.ru/eng/znsl/v278/p63
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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