Limiting distribution of time averages for the additive functionals preset on the semi-Markovian process

• Date: 1990
• Main Authors: Eleiko, Ya. I., Елейко, Я. И.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1990
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8850
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider an additive functional $\zeta_t$ on a continuous time semi-Markov process with an arbitrary state space. We study the existence of the limiting distribution of $\zeta_t/t$ without the condition of the finiteness of the mean occupation time of a fixed state.