
This article is cited in 2 scientific papers (total in 2 papers)
On highlevel crossing for a class of discretetime stochastic processes
E. V. Bulinskaya^{} ^{} M. V. Lomonosov Moscow State University
Abstract:
The aim of this paper is to study the asymptotic behaviour of the first passage time for some discretetime stochastic processes arising in applied probability. The paper is organized as follows. The systems' description is given in § 1 along with the main results. The integervalued random walks with impenetrable (as well as reflecting) barrier at origin
$$
W_{k}=\max(0,W_{k1}+X_{k}), k \geq 1, W_{0}=x
$$
are treated in § 2. The main object of investigation is $N_{x,n}=\inf\{k\colon W_{k}=n\}$, the first overflow time in terms of inventory theory. The limit distribution of normalized random variable $\tau_{x,n}=N_{x,n}(\mathrm{E}N_{x,n})^{1}$ is obtained for all the initial states $x$ and possible values of $\mathrm{E}X_{k}$ for the case of the threevalued i. i. d. random variables $X_{k}$ (demand and supply in batches of fixed volume). The domain of model's stability with respect to initial state and system's parameters is established as well. The influence of twolevel control policy on system's behaviour is dealt with in § 3. It is proved, in particular, that $\tau_{x,n}$ is asymptotically exponential if $\mathrm{E}X_{k}<0$ in a sufficiently wide band in the neighbourhood of the absorbing boundary $n$. The directions of further investigations and various possibilities of application are given in § 4.
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Received: 01.01.1995
Citation:
E. V. Bulinskaya, “On highlevel crossing for a class of discretetime stochastic processes”, Fundam. Prikl. Mat., 1:1 (1995), 81–107
Citation in format AMSBIB
\Bibitem{Bul95}
\by E.~V.~Bulinskaya
\paper On highlevel crossing for a class of discretetime stochastic processes
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 1
\pages 81107
\mathnet{http://mi.mathnet.ru/fpm45}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=1789353}
\zmath{https://zbmath.org/?q=an:0870.60068}
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This publication is cited in the following articles:

Bulinskaya E., “Multilevel control and asymptotic behaviour of some inventory systems”, International Journal of Production Economics, 59:1–3 (1999), 289–295

Bulinskaya E., “Small random perturbations of justintime systems”, International Journal of Production Economics, 71:1–3 (2001), 287–294

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