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A note on first passage functionals for Lévy processes with jumps of rational Laplace transforms. (English) Zbl 1470.60233

Summary: This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time.

MSC:

60J74 Jump processes on discrete state spaces
60G17 Sample path properties
60G51 Processes with independent increments; Lévy processes
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