Functionals of a Lévy Process on Canonical and Generic Probability Spaces

Alexander Steinicke ()
Additional contact information
Alexander Steinicke: University of Innsbruck

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 443-458

Abstract: Abstract We develop an approach to Malliavin calculus for Lévy processes from the perspective of expressing a random variable $$Y$$ Y by a functional $$F$$ F mapping from the Skorohod space of càdlàg functions to $$\mathbb {R}$$ R , such that $$Y=F(X)$$ Y = F ( X ) where $$X$$ X denotes the Lévy process. We also present a chain-rule-type application for random variables of the form $$f(\omega ,Y(\omega ))$$ f ( ω , Y ( ω ) ) . An important tool for these results is a technique which allows us to transfer identities proved on the canonical probability space (in the sense of Solé et al.) associated to a Lévy process with triplet $$(\gamma ,\sigma ,\nu )$$ ( γ , σ , ν ) to an arbitrary probability space $$(\varOmega ,\mathcal {F},\mathbb {P})$$ ( Ω , F , P ) which carries a Lévy process with the same triplet.

Keywords: Lévy processes; Malliavin calculus for Lévy processes; Canonical Lévy process; 60G51; 60G05 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-014-0583-7 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:29:y:2016:i:2:d:10.1007_s10959-014-0583-7

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

DOI: 10.1007/s10959-014-0583-7

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 ().