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2014 Exponential ergodicity of killed Lévy processes in a finite interval
Martin Kolb, Mladen Savov
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Electron. Commun. Probab. 19: 1-9 (2014). DOI: 10.1214/ECP.v19-3006

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 $T_a=\inf\{t>0:\,X_t\notin $. 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 />

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Martin Kolb. Mladen Savov. "Exponential ergodicity of killed Lévy processes in a finite interval." Electron. Commun. Probab. 19 1 - 9, 2014. https://doi.org/10.1214/ECP.v19-3006

Information

Accepted: 24 May 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1312.60057
MathSciNet: MR3216565
Digital Object Identifier: 10.1214/ECP.v19-3006

Subjects:
Primary: 60J35
Secondary: 37A25 , 47A10 , 47D99 , 60G51 , 60J25

Keywords: ‎Banach spaces , ergodicity , Levy processes , Markov processes

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