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

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 P−rMâλ,τâ policy.