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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 4, Pages 847–857 (Mi tvp3517)  

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

Short Communications

On limit theorems on large deviations in narrow zones

L. V. Rozovskiĭ

Leningrad

Abstract: Let $X_1,X_2,…$ be a sequence of independent identically distributed random variables, $S_n=X_1+…+X_n$, $\Phi(x)$ be the standard normal distribution function. We investigate the asymptotics of
$$ \mathbf P\{S_n>x\}/(1-\Phi(x/B_n)),\qquad n\to\infty, $$
for $0\le x\le \Lambda(B_n)$, where the function $\Lambda(z)$ is such that
$$ \Lambda(z)/z\uparrow\infty,\quad\Lambda(z)/z^{1+\varepsilon}\downarrow 0\quad(0<\varepsilon<1,ż>z_0), $$
the sequence $B_n\to\infty$ ($n\to\infty$) and
$$ \sup_{x\ge 0}|\mathbf P\{S_n<xB_n\}-\Phi(x)|=o(1),\qquad n\to\infty. $$


Full text: PDF file (1972 kB)

English version:
Theory of Probability and its Applications, 1982, 26:4, 834–845

Bibliographic databases:

Received: 03.01.1979

Citation: L. V. Rozovskiǐ, “On limit theorems on large deviations in narrow zones”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 847–857; Theory Probab. Appl., 26:4 (1982), 834–845

Citation in format AMSBIB
\Bibitem{Roz81}
\by L.~V.~Rozovski{\v\i}
\paper On limit theorems on large deviations in narrow zones
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 847--857
\mathnet{http://mi.mathnet.ru/tvp3517}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=636782}
\zmath{https://zbmath.org/?q=an:0488.60038|0474.60025}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 834--845
\crossref{https://doi.org/10.1137/1126093}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PM42700019}


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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. L. V. Rozovskii, “Large deviation probabilities for some classes of distributions, satisfying the Cramer condition”, J. Math. Sci. (N. Y.), 128:1 (2005), 2585–2600  mathnet  crossref  mathscinet  zmath
    2. L. V. Rozovskii, “Sums of independent random variables with finite variances – moderate deviations and nonuniform bounds in the CLT”, J. Math. Sci. (N. Y.), 133:3 (2006), 1345–1355  mathnet  crossref  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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