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Local times for spectrally negative Lévy processes. (English) Zbl 1434.60211

Summary: For spectrally negative Lévy processes, adapting an approach from the first author and Z. Palmowski [Stochastic Processes Appl. 128, No. 10, 3273–3299 (2018; Zbl 1401.60087)] we identify joint Laplace transforms involving local times evaluated at either the first passage times, or independent exponential times, or inverse local times. The Laplace transforms are expressed in terms of the associated scale functions. Connections are made with the permanental process and the Markovian loop soup measure.

MSC:

60J55 Local time and additive functionals
60J45 Probabilistic potential theory
60G51 Processes with independent increments; Lévy processes

Citations:

Zbl 1401.60087
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References:

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