A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472.
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Journal Article
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| English
Author
Kolb, MartinLibreCat;
Savov, Mladen
Department
Abstract
We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy
processes for a class of real functions including all continuous functions and for general one-
dimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring
and Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an
open problem. It turns out, that the criterium in the general situation simplifies significantly in
the situation, where the process has a local time, but we also demonstrate that in general our cri-
terium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A.
(2015).
Publishing Year
Journal Title
Bernoulli
Volume
26
Issue
2
Page
1453-1472
LibreCat-ID
Cite this
Kolb M, Savov M. A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. Bernoulli. 2020;26(2):1453-1472. doi:https://doi.org/10.48550/arXiv.1903.03792
Kolb, M., & Savov, M. (2020). A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. Bernoulli, 26(2), 1453–1472. https://doi.org/10.48550/arXiv.1903.03792
@article{Kolb_Savov_2020, title={A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}, volume={26}, DOI={https://doi.org/10.48550/arXiv.1903.03792}, number={2}, journal={Bernoulli}, publisher={Bernoulli Society for Mathematical Statistics and Probability}, author={Kolb, Martin and Savov, Mladen}, year={2020}, pages={1453–1472} }
Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” Bernoulli 26, no. 2 (2020): 1453–72. https://doi.org/10.48550/arXiv.1903.03792.
M. Kolb and M. Savov, “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes,” Bernoulli, vol. 26, no. 2, pp. 1453–1472, 2020, doi: https://doi.org/10.48550/arXiv.1903.03792.
Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” Bernoulli, vol. 26, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2020, pp. 1453–72, doi:https://doi.org/10.48550/arXiv.1903.03792.
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