Limiting distribution of time averages for the additive functionals preset on the semi-Markovian process - Eleiko, Ya. I. (Ukrains’kyi Matematychnyi Zhurnal, 1990)
We consider an additive functional $ζ_t$ on a continuous time semi-Markov process with an arbitrary state space. We study the existence of the limiting distribution of $ζ_t/t$ without the condition of the finiteness of the mean occupation time of a fixed state.