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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
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