English

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

Probability 2019-10-01 v1

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.

Keywords

Cite

@article{arxiv.1909.13311,
  title  = {On Occupation Time for On-Off Processes with Multiple Off-States},
  author = {Chaoran Hu and Vladimir Pozdnyakov and Jun Yan},
  journal= {arXiv preprint arXiv:1909.13311},
  year   = {2019}
}
R2 v1 2026-06-23T11:29:28.698Z