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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
$$
\sup_{x\ge 0}|\mathbf P\{S_n<xB_n\}-\Phi(x)|=o(1),\qquad n\to\infty.
$$
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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
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\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
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\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}
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http://mi.mathnet.ru/eng/tvp3517 http://mi.mathnet.ru/eng/tvp/v26/i4/p847
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This publication is cited in the following articles:
-
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
 -
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
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