On the time a Markov chain spends in a lumped state

On the time a Markov chain spends in a lumped state

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Article ID: iaor1998888
Country: United Kingdom
Volume: 34
Issue: 2
Start Page Number: 340
End Page Number: 345
Publication Date: Jun 1997
Journal: Journal of Applied Probability
Authors:
Abstract:

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 (or 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 (or exponential).

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