A note on Malliavin smoothness on the Lévy space
Abstract
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable
random variables on the Lévy space. We show that when a random variable
satisfies a certain measurability condition, its differentiability and fractional differentiability
can be determined by weighted Lebesgue spaces. The measurability condition
is satisfied for all random variables if the underlying Lévy process is a compound
Poisson process on a finite time interval.
Main Author
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
University of Washington
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201706303191Use this for linking
Review status
Peer reviewed
ISSN
1083-589X
DOI
https://doi.org/10.1214/17-ECP65
Language
English
Published in
Electronic Communications in Probability
Citation
- Laukkarinen, E. (2017). A note on Malliavin smoothness on the Lévy space. Electronic Communications in Probability, 22, Article 34. https://doi.org/10.1214/17-ECP65
License
Copyright© the Author, 2017. This is an open access article distributed under the terms of a Creative Commons License.