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By using limit distribution of Markov
skeleton processes, the article studies homogeneous denumerable
semi-Markov processes and obtains their limit distribution. When the
distribution of renewal interval is non-lattice, the result obtained
in this paper is consistent with that in ,but the
approaches this article used are Markov skeleton processes
approaches which differ from .Furthermore, when the
distribution of renewal interval is lattice, this paper gives the
result, whereas didn't study this case. Finally, this
article generalizes the limit distribution of homogeneous
denumerable semi-Markov processes, and illustrates the result
through one example.