Occupation time distributions for the telegraph process |
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Authors: | Leonid Bogachev Nikita Ratanov |
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Institution: | a Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UKb Facultad de Economía, Universidad del Rosario, Cl.14, No. 4-69, Bogotá, Colombia |
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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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Keywords: | primary 60J27 secondary 60J65 60F05 60K99 |
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