--- res: bibo_abstract: - 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.
@eng bibo_authorlist: - foaf_Person: foaf_givenName: Martin foaf_name: Kolb, Martin foaf_surname: Kolb foaf_workInfoHomepage: http://www.librecat.org/personId=48880 - foaf_Person: foaf_givenName: Mladen foaf_name: Savov, Mladen foaf_surname: Savov bibo_doi: http://dx.doi.org/10.1214/ECP.v19-3006 bibo_issue: '31' bibo_volume: 19 dct_date: 2014^xs_gYear dct_language: eng dct_publisher: Institute of Mathematical Statistics (IMS)@ dct_title: Exponential ergodicity of killed Lévy processes in a finite interval@ ...