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On the Markov renewal theory. (Russian) Zbl 0544.60082
Let M(x,dy,dt) be a nonnegative bounded kernel defined on ($$E\otimes [0,\infty),{\mathcal A}\otimes {\mathcal B})$$ where (E,$${\mathcal A})$$ is a measurable space with $$\sigma$$-algebra $${\mathcal A}$$ and $${\mathcal B}$$ is Borel $$\sigma$$-algebra on $$[0,\infty)$$. The analogues of Frobenius and Smith key renewal theorems for convolutions of $$M(\cdot)$$ are proved.
Reviewer: M.Morozov

##### MSC:
 60K15 Markov renewal processes, semi-Markov processes