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On hitting times for compound Poisson dams with exponential jumps and linear release rate

Part of: Stochastic processes Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Wolfgang Stadje
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email address: mskella@mscc.huji.ac.il
∗∗ Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany.
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Abstract

For a compound Poisson dam with exponential jumps and linear release rate (shot-noise process), we compute the Laplace-Stieltjes transform (LST) and the mean of the hitting time of some positive level given that the process starts from some given positive level. The solution for the LST is in terms of confluent hypergeometric functions of the first and second kinds (Kummer functions).

Keywords

Dam with linear release ratesshot-noise processMarkov processhitting timesconfluent hypergeometric functions

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60G10: Stationary processes 60J25: Continuous-time Markov processes on general state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 781 - 786
Copyright
Copyright © by the Applied Probability Trust 2001 

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Footnotes

This work was supported by the Volkswagen Foundation.

References

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