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Teor. Veroyatnost. i Primenen., 1962, Volume 7, Issue 2, Pages 121–134 (Mi tvp4708)  

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

Limit Theorems for Sums of Independent Variables Taking into Account Large Deviations. III

Yu. V. Linnik

Leningrad

Abstract: Conditions are found which are necessary for uniform normal convergence in the zones $[0,n^\alpha\rho(n)],[- n^\alpha\rho(n)]$ for values of $\alpha \in[\frac{1}{6},\frac{1}{2}]$, and sufficientin the zones $[0,{n^\alpha}/{\rho}(n)],[{-n^\alpha}/{\rho}(n),0]$. The method is a combination of H. Cramer’s method and of the arguments of Part I of this paper.

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English version:
Theory of Probability and its Applications, 1962, 7:2, 115–129

Received: 28.06.1960

Citation: Yu. V. Linnik, “Limit Theorems for Sums of Independent Variables Taking into Account Large Deviations. III”, Teor. Veroyatnost. i Primenen., 7:2 (1962), 121–134; Theory Probab. Appl., 7:2 (1962), 115–129

Citation in format AMSBIB
\Bibitem{Lin62}
\by Yu.~V.~Linnik
\paper Limit Theorems for Sums of Independent Variables Taking into Account Large Deviations.~III
\jour Teor. Veroyatnost. i Primenen.
\yr 1962
\vol 7
\issue 2
\pages 121--134
\mathnet{http://mi.mathnet.ru/tvp4708}
\transl
\jour Theory Probab. Appl.
\yr 1962
\vol 7
\issue 2
\pages 115--129
\crossref{https://doi.org/10.1137/1107012}


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    This publication is cited in the following articles:
    1. D. V. Batkovich, “Local limit theorems for large deviations”, J. Math. Sci. (N. Y.), 188:6 (2013), 641–654  mathnet  crossref  mathscinet
    2. Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “Toward the History of the Saint Petersburg School of Probability and Statistics. i. Limit Theorems For Sums of Independent Random Variables”, Vestnik St. Petersburg Univ. Math., 51:2 (2018), 144–163  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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