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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1997 / Article

Open Access

Volume 10 |Article ID 707613 | https://doi.org/10.1155/S1048953397000415

Jewgeni H. Dshalalow, "On the level crossing of multi-dimensional delayed renewal processes", International Journal of Stochastic Analysis, vol. 10, Article ID 707613, 7 pages, 1997. https://doi.org/10.1155/S1048953397000415

On the level crossing of multi-dimensional delayed renewal processes

Jewgeni H. Dshalalow1

1Department of Applied Mathematics, Florida Institute of Technology, USA

Received01 Feb 1997
Revised01 Aug 1997

Abstract

The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the “crossing level” and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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