Occupation time distributions for the telegraph process

Details Occupation time distributions for the telegraph process Occupation time distributions for the telegraph process

2010-07-19

arxiv.org/abs/1007.3139v1

Mathematics

Probability

23 pages, 4 figures

Scientific paper

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.

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