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Generalized scale functions of standard processes with no positive jumps. (English) Zbl 1445.60065

Summary: As a generalization of scale functions of spectrally negative Lévy processes, we define generalized scale functions of general standard processes with no positive jumps. For this purpose, we utilize the excursion theory. Using the generalized scale functions, we study Laplace transforms of hitting times, potential measures and duality.

MSC:

60J99 Markov processes
60J45 Probabilistic potential theory
60G51 Processes with independent increments; Lévy processes
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