On Continuity Properties of the Law of Integrals of Lévy Processes

By Jean Bertoin, A. Lindner, Ross Maller. 2006

61 citations recorded by the source corpus.

Let (ξ, η) be a bivariate Levy process such that the integral \(\int_0^\infty {e^{ - \xi _{t - } } d\eta _t }\)converges almost surely. We characterise, in terms of their Levy measures, those Levy 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(ξ t ) dt, 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(ξ t ) dY t , where Y is an almost surely strictly increasing stochastic process, independent of ξ.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/8cd76b3effd7cf88cef6acb202969df08c5b8e44

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Citations in the corpus

Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “From [14], we know that the law of IΨ is absolute continuous with a density denoted by fΨ, i.”
On Exponential Functionals of Lévy Processes (2013, background): “2 in [6], hence infinitely divisible so that φV∞(u) 6= 0 for all u ∈ R.”
STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, background): “A necessary and sufficient condition for (2.6) in terms of the generating triplet of {(Xt, Lt)} is found in Erickson and Maller [14].”