---
_id: '33282'
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)."
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Mladen
  full_name: Savov, Mladen
  last_name: Savov
citation:
  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>
  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>
  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} }'
  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>.'
  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>.
  short: M. Kolb, M. Savov, Bernoulli 26 (2020) 1453–1472.
date_created: 2022-09-08T06:36:37Z
date_updated: 2022-09-08T06:48:40Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.1903.03792
intvolume: '        26'
issue: '2'
keyword:
- L ́evy processes
- Perpetual integrals
- Potential measures
language:
- iso: eng
page: 1453-1472
publication: Bernoulli
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
status: public
title: A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
type: journal_article
user_id: '85821'
volume: 26
year: '2020'
...