On Occupation Time for On-Off Processes with Multiple Off-States

2019/09/29 by Hu, Chaoran, Pozdnyakov, Vladimir, Yan, Jun
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.13311

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 understanding such processes. We derive the exact marginal and joint distributions of the off-state occupation times. The theoretical results are confirmed numerically in a simulation study. A special case when all holding times have Levy distribution is considered for the possibility of simplification of the formulas.

Related

• Statistics of the occupation time of renewal processes
• Occupation times of alternating renewal processes with Lévy applications
• Occupation times of general Lévy processes
• The joint distribution of occupation times of skip-free Markov processes and a class of multivariate exponential distributions
• Laws of the iterated logarithm for occupation times of Markov processes