---
_id: '33361'
abstract:
- lang: eng
  text: Following Bertoin who considered the ergodicity and exponential decay of Lévy
    processes in a finite domain, we consider general Lévy processes and their ergodicity
    and exponential decay in a finite interval. More precisely, given Ta=inf{t>0:Xt∉.
    Under general conditions, e.g. absolute continuity of the transition semigroup
    of the unkilled Lévy process, we prove that the killed semigroup is a compact
    operator. Thus, we prove stronger results in view of the exponential ergodicity
    and estimates of the speed of convergence. Our results are presented in a Lévy
    processes setting but are well applicable for Markov processes in a finite interval
    under information about Lebesgue irreducibility of the killed semigroup and that
    the killed process is a double Feller process. For example, this scheme is applicable
    to a work of Pistorius.<br />
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. Exponential ergodicity of killed Lévy processes in a finite
    interval. <i>Electronic Communications in Probability</i>. 2014;19(31):1-9. doi:<a
    href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  apa: Kolb, M., &#38; Savov, M. (2014). Exponential ergodicity of killed Lévy processes
    in a finite interval. <i>Electronic Communications in Probability</i>, <i>19</i>(31),
    1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>
  bibtex: '@article{Kolb_Savov_2014, title={Exponential ergodicity of killed Lévy
    processes in a finite interval}, volume={19}, DOI={<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>},
    number={31}, journal={Electronic Communications in Probability}, publisher={Institute
    of Mathematical Statistics (IMS)}, author={Kolb, Martin and Savov, Mladen}, year={2014},
    pages={1–9} }'
  chicago: 'Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy
    Processes in a Finite Interval.” <i>Electronic Communications in Probability</i>
    19, no. 31 (2014): 1–9. <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  ieee: 'M. Kolb and M. Savov, “Exponential ergodicity of killed Lévy processes in
    a finite interval,” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, pp. 1–9, 2014, doi: <a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.'
  mla: Kolb, Martin, and Mladen Savov. “Exponential Ergodicity of Killed Lévy Processes
    in a Finite Interval.” <i>Electronic Communications in Probability</i>, vol. 19,
    no. 31, Institute of Mathematical Statistics (IMS), 2014, pp. 1–9, doi:<a href="http://dx.doi.org/10.1214/ECP.v19-3006">http://dx.doi.org/10.1214/ECP.v19-3006</a>.
  short: M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.
date_created: 2022-09-14T05:15:00Z
date_updated: 2022-09-14T05:15:06Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1214/ECP.v19-3006
intvolume: '        19'
issue: '31'
language:
- iso: eng
page: 1-9
publication: Electronic Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics (IMS)
status: public
title: Exponential ergodicity of killed Lévy processes in a finite interval
type: journal_article
user_id: '85821'
volume: 19
year: '2014'
...