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 , where is an irreducible Markov chain and is its integral, and (b) the geometric Wiener process where is a Wiener process with non-negative drift and variance parameter . 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 or . The system is controlled by a policy.