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Occupation time distributions for the telegraph process
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Bogachev, Leonid
Ratanov, Nikita
Fecha
2011
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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. © 2011 Elsevier B.V. All rights reserved.
Palabras clave
Arcsine Law , Feynmankac Formula , Laplace Transform , Telegraph Equation , Telegraph Process , Weak Convergence
