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Exponential ergodicity of killed Lévy processes in a finite interval

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Exponential ergodicity of killed Lévy processes in a finite interval
2.	Creator	Author's name, affiliation, country	Martin Kolb; University of Paderborn
2.	Creator	Author's name, affiliation, country	Mladen Svetoslavov Savov; The University of Reading
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Markov processes; Levy processes; ergodicity; Banach spaces;
3.	Subject	Subject classification	60J35; 60J25; 60G51 ; 47D99 ; 47A10; 37A25
4.	Description	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 $T_a=\inf\{t>0:\,X_t\notin (0,a)\}$, $a>0$ and $X$ a Levy process then we study from spectral-theoretical point of view the killed semigroup $P \left(X_t \in . ; T_a > t\right)$. 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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-05-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/3006
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-3006
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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