Donati-Martin, C., Émery, M., Rouault, A. und Stricker, C. (Eds.)
On continuity properties of integrals of Lévy processes
Let (ξ,η) be a bivariate Lévy process such that the integral ∫0∞ e-ξt-dηt
converges almost surely. We characterise, in terms of their Lévy measures, those Lévy processes for which (the distribution of) this integral has atoms. We then turn attention to almost surely convergent integrals of the form I:=∫0∞g(ξt)dYt, where g is a deterministic function. We give sufficient conditions ensuring that I has no atoms, and under further conditions derive that I has a Lebesgue density. The results are also extended to certain integrals of the form ∫0∞g(ξt)dYt, where Y is an almost surely strictly increasing stochastic process, independent of ξ.
Donati-Martin, C., Émery, M., Rouault, A. und Stricker, C.: Séminaire de Probabilités