Duration of stay inside an interval by the poisson process with a negative exponential component

Several two-boundary problems for the Poisson process with an exponential component
 are solved in the present article. The integral transforms of the joint distribution
 of the epoch of the first exit from the interval and the value of the overshoot through boundaries at the epoch of...

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Bibliographic Details
Date:2006
Main Author: Kadankova, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2006
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/4441
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Duration of stay inside an interval by the poisson process with a negative exponential component / T. Kadankova // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 55–67. — Бібліогр.: 11 назв.— англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:Several two-boundary problems for the Poisson process with an exponential component
 are solved in the present article. The integral transforms of the joint distribution
 of the epoch of the first exit from the interval and the value of the overshoot through boundaries at the epoch of the exit are obtained. The Laplace transform of the total duration time of the process’s stay inside the interval is found.
ISSN:0321-3900