The asymptotic behaviour of the cumulative mean of a reward
process Z_{ρ}, where the reward function ρ
belongs to a rather large class of functions, is obtained. It is
proved that EZ_{ρ} (t)=C_{0}+C_{1}t+0(1),t→∞, where C_{0} and C_{1} are fully specified. A section is
devoted to the dual process of a semiMarkov 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.
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