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On weighted occupation times for refracted spectrally negative Lévy processes. (English) Zbl 1404.60066

Summary: For refracted spectrally negative Lévy processes, we identify expressions for several quantities related to the Laplace transforms of their weighted occupation times until first exit times. Such quantities are expressed in terms of the unique solutions to integral equations involving weight functions and scale functions for the associated spectrally negative Lévy processes. Previous results on refracted Lévy processes are recovered.

MSC:

60G51 Processes with independent increments; Lévy processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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