Reward processes for semi-markov processes: asymptotic behaviour

The asymptotic behaviour of the cumulative mean of a reward process Z(rho), where the reward function rho belongs to a rather large class of functions, is obtained, it is proved that EZ(rho)(t) = C-0 + C(1)t + o(1), t --> infinity, where C-0 and C-1 are fully specified. A section is devoted to the dual process of a semi-Markov process, and a formula is given for the mean of the first passage time from a state i to a state j of the dual process, in terms of the means of passage times of the original process.