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

 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
&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:

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}