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

References

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  1. Orsingher, Enzo, 1990. "Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 49-66, February.
  2. Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
  3. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
  4. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
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