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Emptiness times of a dam with stable input and general release function

Published online by Cambridge University Press:  14 July 2016

P. J. Brockwell  and
K. L. Chung
P. J. Brockwell
Affiliation:
La Trobe University
K. L. Chung
Affiliation:
Stanford University
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Abstract

We investigate the nature of the set of emptiness times of a dam whose release rate depends on the content and whose cumulative input process is a pure-jump Lévy process. Detailed results are obtained for stable input processes and release functions of the form r(x) = xβ I(o,∞)(x).

Keywords

DAMSTOCHASTIC INTEGRAL EQUATIONLÉVY ADDITIVE PROCESSZERO SETREGENERATIVE PHENOMENA
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 212 - 217
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Çinlar, E. (1972) A local time for a storage process. Technical Report No. 20, Operations Research Department, Stanford University.Google Scholar
[2] Çinlar, E. and Pinsky, M. (1971) A stochastic integral in storage theory. Z. Wahrscheinlichkeitsth. 17, 227–240.CrossRefGoogle Scholar
[3] Ito, K. (1969) Stochastic Processes , Lecture Note Series, No. 16, Aarhus University.Google Scholar
[4] Kingman, J. F. C. (1973) Homecomings of Markov processes. Adv. Appl. Prob. 5, 66–103.CrossRefGoogle Scholar
[5] Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
[6] Moran, P. A. P. (1969) A theory of dams with continuous input and a general release rule. J. Appl. Prob. 6, 88–98.Google Scholar
[7] Yeo, G. F. (1975) A finite dam with variable release rate. To appear.Google Scholar