{"date_updated":"2022-09-14T05:15:06Z","status":"public","date_created":"2022-09-14T05:15:00Z","abstract":[{"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 />","lang":"eng"}],"intvolume":"        19","_id":"33361","page":"1-9","publication_status":"published","type":"journal_article","language":[{"iso":"eng"}],"user_id":"85821","title":"Exponential ergodicity of killed Lévy processes in a finite interval","year":"2014","doi":"http://dx.doi.org/10.1214/ECP.v19-3006","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>","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} }","short":"M. Kolb, M. Savov, Electronic Communications in Probability 19 (2014) 1–9.","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>.","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>.","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>"},"publication":"Electronic Communications in Probability","author":[{"last_name":"Kolb","full_name":"Kolb, Martin","id":"48880","first_name":"Martin"},{"first_name":"Mladen","last_name":"Savov","full_name":"Savov, Mladen"}],"department":[{"_id":"96"}],"publisher":"Institute of Mathematical Statistics (IMS)","issue":"31","volume":19}