{"volume":26,"doi":"https://doi.org/10.48550/arXiv.1903.03792","abstract":[{"lang":"eng","text":"We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy\r\nprocesses for a class of real functions including all continuous functions and for general one-\r\ndimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring\r\nand Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an\r\nopen problem. It turns out, that the criterium in the general situation simplifies significantly in\r\nthe situation, where the process has a local time, but we also demonstrate that in general our cri-\r\nterium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A.\r\n(2015)."}],"keyword":["L ́evy processes","Perpetual integrals","Potential measures"],"page":"1453-1472","type":"journal_article","publication":"Bernoulli","issue":"2","date_created":"2022-09-08T06:36:37Z","author":[{"last_name":"Kolb","full_name":"Kolb, Martin","first_name":"Martin","id":"48880"},{"first_name":"Mladen","full_name":"Savov, Mladen","last_name":"Savov"}],"status":"public","intvolume":"        26","_id":"33282","year":"2020","department":[{"_id":"96"}],"citation":{"apa":"Kolb, M., &#38; Savov, M. (2020). A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. <i>Bernoulli</i>, <i>26</i>(2), 1453–1472. <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>","ieee":"M. Kolb and M. Savov, “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes,” <i>Bernoulli</i>, vol. 26, no. 2, pp. 1453–1472, 2020, doi: <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>.","mla":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” <i>Bernoulli</i>, vol. 26, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2020, pp. 1453–72, doi:<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>.","bibtex":"@article{Kolb_Savov_2020, title={A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}, volume={26}, DOI={<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>}, number={2}, journal={Bernoulli}, publisher={Bernoulli Society for Mathematical Statistics and Probability}, author={Kolb, Martin and Savov, Mladen}, year={2020}, pages={1453–1472} }","ama":"Kolb M, Savov M. A Characterization of the Finiteness of Perpetual Integrals of Levy Processes. <i>Bernoulli</i>. 2020;26(2):1453-1472. doi:<a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>","chicago":"Kolb, Martin, and Mladen Savov. “A Characterization of the Finiteness of Perpetual Integrals of Levy Processes.” <i>Bernoulli</i> 26, no. 2 (2020): 1453–72. <a href=\"https://doi.org/10.48550/arXiv.1903.03792\">https://doi.org/10.48550/arXiv.1903.03792</a>.","short":"M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472."},"publisher":"Bernoulli Society for Mathematical Statistics and Probability","user_id":"85821","title":"A Characterization of the Finiteness of Perpetual Integrals of Levy Processes","publication_status":"published","date_updated":"2022-09-08T06:48:40Z","language":[{"iso":"eng"}]}