An alternative approach to the analysis of finite semi-markov and related processes

Let J(t) be a finite semi-Markov process associated with the age process X(t) and the reward process Z(t). Bystudying the probabilistic flow of the trivariate process in its state space, new transform results are obtained. Some known results are then derived directly from these transform results, thereby providing an alternative approach for analysis of semi-Markov and related processes. Some new results are also obtained regarding the reward process Z(t) and its first passage times.