Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T16:58:02.807Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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