Perturbation theory for semi-Markov control problems

In earlier work, the authors considered the perturbation of systems undergoing Markov processes in which the times between two consecutive decision time points were equidistant. They now consider perturbations of processes for which the times between transition are random variables. These are called semi-Markov processes. A semi-Markov control process is observed at decision time points t=0.1,. . .; starting at t=0. At each decision time point the system is one of a finite number of states and an action has to be chosen. The discounted semi-Markov control problem and the limiting average semi-Markov control problem are considered