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A potential-theoretical review of some exit problems of spectrally negative Lévy processes. (English) Zbl 1065.60047
Émery, Michel (ed.) et al., 38th seminar on probability. Dedicated Jacques Azéma on the occasion on his 65th birthday. Berlin: Springer (ISBN 3-540-23973-1/pbk). Lecture Notes in Mathematics 1857, 30-41 (2005).
The author considers first exit problems for a spectrally negative Lévy process, that is, a stochastic process with càdlàg paths without positive jumps that has stationary independent increments. He shows that probabilistic potential theory allows a simple solution to these problems, which have been solved by other methods.
For the entire collection see [Zbl 1055.60001].

60G51 Processes with independent increments; Lévy processes
60J45 Probabilistic potential theory