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On non-singular Markov renewal processes with an application to a growth–catastrophe model

  • Seppo Niemi (a1)

Abstract

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.

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Postal address: Department of Mathematics, University of Helsinki, Hallituskatu 15, 00100 Helsinki 10, Finland.

References

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On non-singular Markov renewal processes with an application to a growth–catastrophe model

  • Seppo Niemi (a1)

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