Exponential ergodicity of killed Lévy processes in a finite interval Kolb, Martin Savov, Mladen 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 /> Institute of Mathematical Statistics (IMS) 2014 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/33361 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> eng info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1214/ECP.v19-3006 info:eu-repo/semantics/closedAccess