On several two-boundary problems for a particular class of Lévy processes. (English) Zbl 1138.60038

Kadankova, T.; Veraverbeke, N.

J. Theor. Probab. 20, No. 4, 1073-1085 (2007).

The authors study the joint law of the first exit time and the overshoot from an interval for a special class of Lévy processes; more specifically, the authors consider a compound Poisson process with exponentially distributed negative jumps and arbitrary positive jumps. The special structure of this Lévy processes allows them to derive closed form expressions for the integral transform of this joint law. In addition, the authors study the joint law of the entry into an interval and the value of the process at the entry time for the same class of processes.

Reviewer: Antonis Papapantoleon (Wien)

MSC:

60G51	Processes with independent increments; Lévy processes
60J50	Boundary theory for Markov processes

Keywords:

compound Poisson process with two sided jumps; first exit time; overshoot; first entry time; integral transforms

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