TY - GEN

T1 - On continuity properties of the law of integrals of Lévy processes

AU - Bertoin, Jean

AU - Lindner, Alexander

AU - Maller, Ross

PY - 2008

Y1 - 2008

N2 - Let (ξ, η) be a bivariate Lévy process such that the integral 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(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.

AB - Let (ξ, η) be a bivariate Lévy process such that the integral 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(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.

UR - http://www.scopus.com/inward/record.url?scp=51849127412&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-77913-1_6

DO - 10.1007/978-3-540-77913-1_6

M3 - Conference contribution

AN - SCOPUS:51849127412

SN - 9783540779124

T3 - Lecture Notes in Mathematics

SP - 137

EP - 159

BT - Seminaire de Probabilites XLI

PB - Springer Verlag

ER -