A Smooth Approach to Malliavin Calculus for Lévy Processes

Horst Osswald ()
Additional contact information
Horst Osswald: Mathematisches Institut der Universität München

Journal of Theoretical Probability, 2009, vol. 22, issue 2, 441-473

Abstract: Abstract An approach to Malliavin calculus for Lévy processes, discrete in time and smooth in chance, is presented. Each Lévy triple can be satisfied by a Lévy process living on a fixed sample space Ω, which is, in a certain sense, a finite dimensional Euclidean space. The probability measures on Ω characterize the Lévy processes. We compare these measures with the associated Lévy measures, and present several examples. Using chaos expansions for Lévy functionals, even for those having no moments, we can represent all these functionals by polynomials in several variables. There exists an effective method to compute the kernels of the chaos decomposition. Finally, we point out several applications, which are postponed to a succession of papers.

Keywords: Malliavin calculus; Lévy processes; Chaos decomposition; 60H07; 60H40; 60G51; 26E35 (search for similar items in EconPapers)
Date: 2009
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/s10959-008-0148-8 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:22:y:2009:i:2:d:10.1007_s10959-008-0148-8

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

DOI: 10.1007/s10959-008-0148-8

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 ().