English

Occupation time distributions for the telegraph process

Probability 2010-07-20 v1

Abstract

For the one-dimensional telegraph process, we obtain explicit distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process is in the range of sub-normal or normal deviations from the origin; in the former case, the limit is given by the arcsine law. These limit theorems are also extended to the case of more general occupation-type functionals.

Keywords

Cite

@article{arxiv.1007.3139,
  title  = {Occupation time distributions for the telegraph process},
  author = {Leonid Bogachev and Nikita Ratanov},
  journal= {arXiv preprint arXiv:1007.3139},
  year   = {2010}
}

Comments

23 pages, 4 figures

R2 v1 2026-06-21T15:49:46.530Z