On Exponential Functionals of Lévy Processes

Anita Behme () and Alexander Lindner ()
Additional contact information
Anita Behme: Technische Universität München
Alexander Lindner: Technische Universität Braunschweig

Journal of Theoretical Probability, 2015, vol. 28, issue 2, 681-720

Abstract: Abstract Exponential functionals of Lévy processes appear as stationary distributions of generalized Ornstein–Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process. Further, we use these results to investigate properties of the mapping $$\Phi $$ Φ , which maps two independent Lévy processes to their corresponding exponential functional, where one of the processes is assumed to be fixed. We show that in many cases this mapping is injective, and give the inverse mapping in terms of (Lévy) characteristics. Also, continuity of $$\Phi $$ Φ is treated, and some results on its range are obtained.

Keywords: Generalized Ornstein–Uhlenbeck process; Lévy process; Feller process; Infinitesimal generator; Integral mapping; Stationarity; 60G10; 60G51; 60J35 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-013-0507-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:28:y:2015:i:2:d:10.1007_s10959-013-0507-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-013-0507-y

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().