RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1977, Volume 22, Issue 5, Pages 763–770 (Mi mz8098)  

Distribution of the supremum of sums of independent variables with negative drift

M. S. Sgibnev

Institute of Mathematics, Siberian Branch of USSR Academy of Sciences

Abstract: Let $\{\xi_n\}$ be a sequence of identically distributed independent random variables, $M\xi_1=\mu<0$, $M\xi_1^2<\infty$; $S_0=0$, $S_n=\xi_1+\xi_2+…+=xi_n$, $n\ge1$; $\overline S=\sup\{S_n:n\ge0\}$. The asymptotic behavior of $P(\overline S\ge t)$ as $t\to\infty$ is studied. If $\int_t^\infty P(\xi_1\ge x) dx=O(\tau(t))$, then
$$ P(\overline S\ge t)-\frac1{|\mu|}\int_t^\infty P(\xi_1\ge x) dx=O(\tau(t)/t), $$
$\tau(t)$ is a positive function, having regular behavior at infinity.

Full text: PDF file (450 kB)

English version:
Mathematical Notes, 1977, 22:5, 916–920

Bibliographic databases:

UDC: 519.2
Received: 14.01.1977

Citation: M. S. Sgibnev, “Distribution of the supremum of sums of independent variables with negative drift”, Mat. Zametki, 22:5 (1977), 763–770; Math. Notes, 22:5 (1977), 916–920

Citation in format AMSBIB
\Bibitem{Sgi77}
\by M.~S.~Sgibnev
\paper Distribution of the supremum of sums of independent variables with negative drift
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 763--770
\mathnet{http://mi.mathnet.ru/mz8098}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=467931}
\zmath{https://zbmath.org/?q=an:0373.60061}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 916--920
\crossref{https://doi.org/10.1007/BF01098358}


Linking options:
  • http://mi.mathnet.ru/eng/mz8098
  • http://mi.mathnet.ru/eng/mz/v22/i5/p763

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:145
    Full text:57
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020