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






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


Teor. Veroyatnost. i Primenen., 1978, Volume 23, Issue 4, Pages 705–714 (Mi tvp3106)  

Ergodic and stability theorems for random walks in the strip and their applications

A. A. Borovkov

Novosibirsk

Abstract: Let $\{N_n,\tau_n^e,\tau_n^s; 1\le n<\infty\}$ be a stationary sequence of positive random variables, $\xi_n=\tau_n^s-\tau_n^e$. In this paper ergodic and stability theorems are obtained for the sequences $\{w_{n+k}; k\ge 0\}$ as $n\to\infty$, which are defined by the recurrent equations of two types. The equations of the first type have the form
\begin{align*} &w_{n+1}=\max(0,w_n+y_n),\qquad n\ge 1,
&where y_n= \begin{cases} \xi_n,&if w_n\le N_n,
-\tau_n^e,&if w_n> N_n. \end{cases} \end{align*}
The equations of the second type are the following:
$$ w_{n+1}=\min\{N_{n+1},\max(0,w_n+\xi_n)\},\qquad n\ge 1. $$
The applications to the queueing theory are considered.

Full text: PDF file (645 kB)

English version:
Theory of Probability and its Applications, 1979, 23:4, 677–685

Bibliographic databases:

Received: 20.05.1977

Citation: A. A. Borovkov, “Ergodic and stability theorems for random walks in the strip and their applications”, Teor. Veroyatnost. i Primenen., 23:4 (1978), 705–714; Theory Probab. Appl., 23:4 (1979), 677–685

Citation in format AMSBIB
\Bibitem{Bor78}
\by A.~A.~Borovkov
\paper Ergodic and stability theorems for random walks in the strip and their applications
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 4
\pages 705--714
\mathnet{http://mi.mathnet.ru/tvp3106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=516269}
\zmath{https://zbmath.org/?q=an:0421.60083|0388.60093}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 23
\issue 4
\pages 677--685
\crossref{https://doi.org/10.1137/1123085}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1978JA77700001}


Linking options:
  • http://mi.mathnet.ru/eng/tvp3106
  • http://mi.mathnet.ru/eng/tvp/v23/i4/p705

    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
    Erratum
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:215
    Full text:84

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