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.
Djilali Ait-Aoudia. "A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms." Abstr. Appl. Anal. 2016 1 - 8, 2016. https://doi.org/10.1155/2016/5914657