On several two-boundary problems for a particular class of Lévy processes

Details On several two-boundary problems for a particular class of Lévy processes On several two-boundary problems for a particular class of Lévy processes

2007-01-31

arxiv.org/abs/math/0701924v1

Mathematics

Probability

10 pages

Scientific paper

Several two-boundary problems are solved for a special L\'{e}vy process: the Poisson process with an exponential component. The jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is arbitrary, while the distribution of the negative jumps is exponential. Closed form expressions are obtained for the integral transforms of the joint distribution of the first exit time from an interval and the value of the overshoot through boundaries at the first exit time. Also the joint distribution of the first entry time into the interval and the value of the process at this time instant are determined in terms of integral transforms.

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