Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T19:29:56.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolvent operators of Markov processes and their applications in the control of a finite dam

Published online by Cambridge University Press:  14 July 2016

F. A. Attia
F. A. Attia*
Affiliation:
Kuwait University
*
∗ Postal address: Department of Mathematics, Kuwait University, P.O. Box 5969, Kuwait.
Get access Rights & Permissions [Opens in a new window]

Abstract

The resolvent operators of the following two processes are obtained: (a) the bivariate Markov process W = (X, Y), where Y(t) is an irreducible Markov chain and X(t) is its integral, and (b) the geometric Wiener process G(t) = exp{B(t} where B(t) is a Wiener process with non-negative drift μ and variance parameter σ2. These results are then used via a limiting procedure to determine the long-run average cost per unit time of operating a finite dam where the input process is either X(t) or G(t). The system is controlled by a policy (Attia [1], Lam [6]).

Keywords

INTEGRAL OF A MARKOV CHAINGEOMETRIC WIENER PROCESSKERNELSTOPPING TIMECOST FUNCTIONAL
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 314 - 324
Copyright
Copyright © Applied Probability Trust 1989 

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.)

Footnotes

Research supported by Kuwait University Research Grant No. SM 050 and Kuwait Foundation for the Advancement of Sciences Grant No. 87–09–01.

References

[1] Attia, F. A. (1987) The control of a finite dam with penalty cost function: Markov input rate. J. Appl. Prob. 24, 457–465.Google Scholar
[2] Attia, F. A. and Brockwell, P. J. (1982) The control of a finite dam. J. Appl. Prob. 19, 815–825.Google Scholar
[3] Faddy, M. J. (1974) Optimal control of finite dams: discrete (2-stage) output procedure. J. Appl. Prob. 11, 111–121.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
[5] Karlin, S. and Taylor, H. M. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
[6] Yeh, Lam (1985) Optimal control of a finite dam: average cost case. J. Appl. Prob. 22, 480–484.CrossRefGoogle Scholar
[7] Yeh, Lam and Hua, Lou Jiann (1987) Optimal control of a finite dam — Wiener process input. J. Appl. Prob. 24, 186–199.Google Scholar
[8] Zuckerman, D. (1977) Two-stage output procedure of a finite dam. J. Appl. Prob. 14, 421–425.Google Scholar