RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

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

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 $Ñ$ is a constant.

Full text: PDF file (213 kB)

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tvp645
• http://mi.mathnet.ru/eng/tvp/v11/i3/p497

 SHARE:

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. A. E. Kuznetsov, “Analytical proof of Pecherskii–Rogozin identity and Wiener–Hopf factorization”, Theory Probab. Appl., 55:3 (2011), 432–443
•  Number of views: This page: 155 Full text: 78