On the time a Markov chain spends in a lumped state
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The sojourn time that a Markov chain spends in a subset E of its state space has a distribution that depends on the hitting distribution on E and the probabilities (resp. rates in the continuous-time case) that govern the transitions within E. In this note we characterise the set of all hitting distributions for which the sojourn time distribution is geometric (resp. exponential).
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2005 ◽
Vol 37
(4)
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pp. 1015-1034
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1997 ◽
Vol 29
(01)
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pp. 92-113
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1989 ◽
Vol 12
(9)
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pp. 1167-1173
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2016 ◽
Vol 4
(6)
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pp. 547-559