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Teor. Veroyatnost. i Primenen., 1982, Volume 27, Issue 3, Pages 474–491 (Mi tvp2380)  

This article is cited in 2 scientific papers (total in 2 papers)

Large deviations of stochastic processes close to the Gaussian ones

V. I. Piterbarg

Moscow

Abstract: Asymptotic expansions for the probability $\displaystyle\mathbf P\{\max_{t\in[0,T]}X_{(n)}(t)>u\}$ when $u\to\infty$ or $u, T\to\infty$ are given. It is supposed that the random process $X_{(n)}$ is close to the Gaussian process in some sense and is smooth enough in mean quadratic. As an example of application we consider the central limit theorem for random processes which are smooth in mean quadratic and for the noise-process.

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English version:
Theory of Probability and its Applications, 1983, 27:3, 504–524

Bibliographic databases:

Received: 05.02.1980

Citation: V. I. Piterbarg, “Large deviations of stochastic processes close to the Gaussian ones”, Teor. Veroyatnost. i Primenen., 27:3 (1982), 474–491; Theory Probab. Appl., 27:3 (1983), 504–524

Citation in format AMSBIB
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\by V.~I.~Piterbarg
\paper Large deviations of stochastic processes close to the Gaussian ones
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 3
\pages 474--491
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=673920}
\zmath{https://zbmath.org/?q=an:0517.60029|0495.60036}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 3
\pages 504--524
\crossref{https://doi.org/10.1137/1127059}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RJ51700006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Adler R.J., “On excursion sets, tube formulas and maxima of random fields”, Annals of Applied Probability, 10:1 (2000), 1–74  mathscinet  zmath  isi
    2. M. S. Muminov, “On approximating the probability of a large excursion of a nonstationary Gaussian process”, Siberian Math. J., 51:1 (2010), 144–161  mathnet  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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