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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 203–206 (Mi tvp2701)  

Short Communications

On property of “waiting process”

V. A. Labkovskii

Moscow

Abstract: Let $X_1,X_2,…$ be i.i.d. integer random variables with $-\infty\le\mathbf EX_1<0$ and $\mathbf P\{X_1>0\}>0$. Consider the process $W_t$, $t=0,1,…$, defined by formula:
$$ W_0=0,\quad W_{t+1}=\max\{W_t+X_{t+1};0\}, $$
and its passage time $\tau(N)=\min\{t\colon W_t\ge N\}$, $N=1,2,…$. In this paper the existence of $\lim\sqrt[N]{\mathbf E\tau(N)}$ is proved, and its value is found.

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English version:
Theory of Probability and its Applications, 1973, 18:1, 196–198

Bibliographic databases:

Received: 14.03.1972

Citation: V. A. Labkovskii, “On property of “waiting process””, Teor. Veroyatnost. i Primenen., 18:1 (1973), 203–206; Theory Probab. Appl., 18:1 (1973), 196–198

Citation in format AMSBIB
\Bibitem{Lab73}
\by V.~A.~Labkovskii
\paper On property of ``waiting process''
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 203--206
\mathnet{http://mi.mathnet.ru/tvp2701}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=324791}
\zmath{https://zbmath.org/?q=an:0282.60067}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 196--198
\crossref{https://doi.org/10.1137/1118021}


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