On non-singular Markov renewal processes with an application to a growth–catastrophe model
Keyword(s):
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.
1964 ◽
Vol 35
(4)
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pp. 1746-1764
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1999 ◽
Vol 51
(2)
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pp. 369-382
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1999 ◽
Vol 36
(2)
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pp. 415-432
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1976 ◽
Vol 8
(03)
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pp. 531-547
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Keyword(s):
1991 ◽
Vol 57
(4)
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pp. 3286-3301
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Keyword(s):