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Diskr. Mat., 2004, Volume 16, Issue 1, Pages 140–145 (Mi dm148)  

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

On the probabilities of large deviations of the Shepp statistic

A. M. Kozlov


Abstract: We find the asymptotic behaviour of the probability of large deviations $\mathsf P(W_{L,L}\geq\theta L)$ of the Shepp statistic $W_{L,L}$ which is equal to the maximum of fluctuations of the random walk
$$ S_n=\sum_{i=1}^n\xi_i $$
in the window of width $L$ moving in the interval $[1,2L]$ as $L\to\infty$ and $\theta$ is a constant. We assume that $\xi_1,\xi_2,\ldots$ are independent identically distributed random variables with non-lattice distribution satisfying the right-side Cramer condition. We show that the asymptotics are of the form $H_\theta L\mathsf P(S_l\geq\theta L)$, where $H_\theta$ is a constant depending on $\theta$.
This research was supported by the Russian Foundation for Basic Research, grant 01–0100–649.

DOI: https://doi.org/10.4213/dm148

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English version:
Discrete Mathematics and Applications, 2004, 14:2, 211–216

Bibliographic databases:

UDC: 519.2
Received: 20.01.2004

Citation: A. M. Kozlov, “On the probabilities of large deviations of the Shepp statistic”, Diskr. Mat., 16:1 (2004), 140–145; Discrete Math. Appl., 14:2 (2004), 211–216

Citation in format AMSBIB
\Bibitem{Koz04}
\by A.~M.~Kozlov
\paper On the probabilities of large deviations of the Shepp statistic
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 1
\pages 140--145
\mathnet{http://mi.mathnet.ru/dm148}
\crossref{https://doi.org/10.4213/dm148}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069995}
\zmath{https://zbmath.org/?q=an:1050.60025}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 2
\pages 211--216
\crossref{https://doi.org/10.1515/156939204872356}


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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. Zholud D., “Extremes of Shepp statistics for Gaussian random walk”, Extremes, 12:1 (2009), 1–17  crossref  mathscinet  zmath  isi  elib  scopus
    2. Tan ZhongQuan, Yang Yang, “Extremes of Shepp Statistics For Fractional Brownian Motion”, Sci. China-Math., 58:8 (2015), 1779–1794  crossref  mathscinet  zmath  isi  elib  scopus
  • Дискретная математика
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