Occupation time distributions for the telegraph process

Leonid Bogachev, Nikita Ratanov

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


For the one-dimensional telegraph process, we obtain explicitly the 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 subnormal 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.

Original languageEnglish (US)
Pages (from-to)1816-1844
Number of pages29
JournalStochastic Processes and their Applications
Issue number8
StatePublished - Aug 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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