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

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...

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Bibliographic Details
Published inModern Stochastics: Theory and Applications Vol. 9; no. 4; pp. 413 - 430
Main Authors Hu, Chaoran, Pozdnyakov, Vladimir, Yan, Jun
Format Journal Article
LanguageEnglish
Published VTeX 01.11.2022
Subjects
Lévy distribution
Markov renewal process
telegraph process
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Summary: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.
ISSN:2351-6046
2351-6054
DOI:10.15559/22-VMSTA210