On occupation time for on-off processes with multiple off-states
Volume 9, Issue 4 (2022), pp. 413–430
Pub. online: 21 June 2022
Type: Research Article
Open Access
Open Access
Received
15 January 2022
15 January 2022
Revised
9 April 2022
9 April 2022
Accepted
5 June 2022
5 June 2022
Published
21 June 2022
21 June 2022
Abstract
The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two off-states jointly is crucial to understand such processes. The exact marginal and joint distributions of the off-state occupation times are derived. The theoretical results are confirmed numerically in a simulation study. A special case when all holding times have Lévy distribution is considered for the possibility of simplification of the formulas.
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