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Occupation time distributions for the telegraph process

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  • Bogachev, Leonid
  • Ratanov, Nikita

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 121 (2011)
Issue (Month): 8 (August)
Pages: 1816-1844

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Handle: RePEc:eee:spapps:v:121:y:2011:i:8:p:1816-1844

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Related research

Keywords: Telegraph process Telegraph equation Feynman-Kac formula Weak convergence Arcsine law Laplace transform;

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