Local Times for Spectrally Negative Lévy Processes
For spectrally negative Lévy processes, adapting an approach from Li and Palmowski (Stoch. Process. Appl. 128(10), 3273–3299 2018) 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.
KeywordsSpectrally negative Lévy process Local time Inverse local time Weighted occupation time Permanental process Markovian loop soup measure
Mathematics Subject Classification (2010)60J55 60J45 60G51
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We are grateful to an anonymous referee for numerous very helpful comments and suggestions. Bo Li thanks Concordia University where the work on this paper was carried out during his visits.
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