Limiting distributions of time averages of additive functionals defined on a semi-Markov process

We consider an additive functional _ton a continuous time semi-Markov process with an arbitrary state space. We study the existence of the limiting distribution of _t/t without the condition of the finiteness of the mean occupation time of a fixed state.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 843–847, June, 1990.