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On occupation time for on-off processes with multiple off-states

Published: 21 June 2022
 by  VTeX

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.
Keywords: numerically in a simulation / occupation time / model / jointly / theoretical / holding / Lévy / simplification
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