The control of a finite dam with penalty cost function: Wiener process input

F. A. Attia

Stochastic Processes and their Applications, 1987, vol. 25, 289-299

Abstract: The long-run average cost per unit time of operating a finite dam controlled by a P[tau],[lambda]M policy (Attia, 1987) is determined when the cumulative input process is a Wiener process with drift. A penalty cost which accrues continuously at the rate g(Z(t)), where g is a bounded measurable function of the content, is also introduced. We first obtain the resolvent operator R[alpha] of a Wiener process with a reflecting boundary at 0 and the expansion of the associated kernel K[alpha] as a power series in [alpha]. Then we use these results to determine the long-run average cost per unit time.

Keywords: reflected; Wiener; process; generators; resolvent; operators; finite; dam; stopping; time; occupation; time; Laplace; transform (search for similar items in EconPapers)
Date: 1987
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