A Characterization of the Finiteness of Perpetual Integrals of Levy Processes Kolb, Martin Savov, Mladen L ́evy processes Perpetual integrals Potential measures 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). Bernoulli Society for Mathematical Statistics and Probability 2020 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/33282 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> eng info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.48550/arXiv.1903.03792 info:eu-repo/semantics/closedAccess