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). By studying the probabilistic flow of the trivariate process Y(t) = [ J ( t ), X( t ), Z ( t ) ] 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.