Delay differential equations driven by Lévy processes: Stationarity and Feller properties
We consider a stochastic delay differential equation driven by a general Lévy process. Both the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov-Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established.
Volume (Year): 116 (2006)
Issue (Month): 10 (October)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gushchin, Alexander A. & Küchler, Uwe, 1998.
"On stationary solutions of delay differential equations driven by a Lévy process,"
SFB 373 Discussion Papers
1998,98, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Gushchin, Alexander A. & Küchler, Uwe, 2000. "On stationary solutions of delay differential equations driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 195-211, August.
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:116:y:2006:i:10:p:1409-1432. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.