Cumulant Operators for Lie–Wiener–Itô–Poisson Stochastic Integrals

Nicolas Privault

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 269-298

Abstract: Abstract The classical combinatorial relations between moments and cumulants of random variables are generalized into covariance-moment identities for stochastic integrals and divergence operators. This approach is based on cumulant operators defined by the Malliavin calculus in a general framework that includes Itô–Wiener and Poisson stochastic integrals as well as the Lie–Wiener path space. In particular, this allows us to recover and extend various characterizations of Gaussian and infinitely divisible distributions.

Keywords: Moments; Cumulants; Stochastic integrals; Malliavin calculus; Wiener space; Path space; Lie groups; Poisson space; 60H07; 60H05 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-013-0532-x 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:1:d:10.1007_s10959-013-0532-x

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

DOI: 10.1007/s10959-013-0532-x

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 ().