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Occupation times of spectrally negative Lévy processes with applications. (English) Zbl 1227.60061
Summary: We compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Lévy processes. Our results are extensions of known results for standard Brownian motion and jump-diffusion processes. The results are expressed in terms of the so-called scale functions of the spectrally negative Lévy process and its Laplace exponent. Applications to insurance risk models are also presented.

60G51 Processes with independent increments; Lévy processes
60E10 Characteristic functions; other transforms
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