Fluctuation identities for spectrally negative Lévy processes killed by general additive functionals are expressed via generalized scale functions that solve Volterra-type integral equations driven by Radon measures.
Characterization and convergence.Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics.John Wiley & Sons, Inc., New York.(1986)
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Fluctuation theory for spectrally negative L\'evy processes killed by additive functionals
Fluctuation identities for spectrally negative Lévy processes killed by general additive functionals are expressed via generalized scale functions that solve Volterra-type integral equations driven by Radon measures.