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On dams with additive inputs and a general release rule

Published online by Cambridge University Press:  14 July 2016

E. Çinlar  and
M. Pinsky
E. Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
M. Pinsky
Affiliation:
Northwestern University, Evanston, Illinois
*
* Now at Stanford University.
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Abstract

An infinite capacity dam subject to an additive input process and a general release rule is considered. The input process can have infinitely many jumps in any finite interval, and the rate of release is r(x) when the dam content is x. The content is constructed as the increasing limit of a sequence of Markov processes and the convergence is shown to be almost surely uniform over finite intervals. The limit process is shown to be a standard Markov process and its characteristic equation is computed.

Keywords

CONTINUOUS DAMSMARKOV PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 422 - 429
Copyright
Copyright © Applied Probability Trust 1972 

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Footnotes

Research supported by National Science Foundation Grants GK-4196 and GP-9437.

References

[1] Blumenthal, R. M. and Getoor, R. K. (1968) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
[2] Çinlar, E. (1971) On dams with continuous semi-Markovian inputs. J. Math. Anal. Appl. 35, 434–448.CrossRefGoogle Scholar
[3] Çinlar, E. and Pinsky, M. (1971) A stochastic integral in storage theory. Z. Wahrscheinlichkeitsth. 17, 227–240.CrossRefGoogle Scholar
[4] Hida, T. (1970) Stationary Stochastic Processes. Math. Notes, Princeton University Press, Princeton.Google Scholar
[5] Moran, P. A. P. (1956) A probability theory of a dam with a continuous release rule. Quart. J. Math. Oxford Ser. 7, 130–137.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