Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities

In the present paper, the reward paths in non homogeneous semi-Markov systems in discrete time are examined with stochastic selection of the transition probabilities. The mean entrance probabilities and the mean rewards in the course of time are evaluated. Then the rate of the total reward for the homogeneous case is examined and the mean total reward is evaluated by means of p.g.f’s.