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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.
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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 

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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

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