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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 3, Pages 497–500 (Mi tvp645)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

The accuracy of approximation oi the limit distribution to the distribution of the maximum of sums of independent random variables

B. A. Rogozin

Novosibirsk

Abstract: Let $\xi_1\xi_2,…$ be a sequence of identically distributed independent random variables n and $S_0=0$, $S_n=\sum_{k=1}^n\xi_k$, $n=1,2,…$, $\bar S_n=\max_{0\le k\le n}S_k$, $n=0,1…$. Let us suppose that $\mathbf M\xi_1=a>0$, $\beta_3=\mathbf M|\xi_1-a|^3<\infty$, and denote $\sigma^2=\mathbf M(\xi_1-a)^2$. It is established that
$$ \mathbf P\{S_n\le x\}-\mathbf P\{\bar S_n\le x\}\le\frac C{\sqrt n}\max\{\frac{\beta_3^2}{\sigma^6},\frac{\beta_3^2}{a^6},\frac{(\mathbf M|\xi_1|)^2}{\sigma^2}\} $$
where $С$ is a constant.

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English version:
Theory of Probability and its Applications, 1966, 11:3, 438–441

Bibliographic databases:

Received: 04.08.1965

Citation: B. A. Rogozin, “The accuracy of approximation oi the limit distribution to the distribution of the maximum of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 11:3 (1966), 497–500; Theory Probab. Appl., 11:3 (1966), 438–441

Citation in format AMSBIB
\Bibitem{Rog66}
\by B.~A.~Rogozin
\paper The accuracy of approximation oi the limit distribution to the distribution of the maximum of sums of independent random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 3
\pages 497--500
\mathnet{http://mi.mathnet.ru/tvp645}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=198530}
\zmath{https://zbmath.org/?q=an:0202.48504}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 3
\pages 438--441
\crossref{https://doi.org/10.1137/1111043}


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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. A. E. Kuznetsov, “Analytical proof of Pecherskii–Rogozin identity and Wiener–Hopf factorization”, Theory Probab. Appl., 55:3 (2011), 432–443  mathnet  crossref  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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