An Itō Formula in the Space of Tempered Distributions

Suprio Bhar ()
Additional contact information
Suprio Bhar: Indian Statistical Institute Bangalore Centre

Journal of Theoretical Probability, 2017, vol. 30, issue 2, 510-528

Abstract: Abstract We extend the Itō formula (Rajeev in From Tanaka’s formula to Ito’s formula: distributions, tensor products and local times, Springer, Berlin, 2001, Theorem 2.3) for semimartingales with paths that are right continuous and have left limits. We also comment on the local time process of such semimartingales. We apply the Itō formula to Lévy processes to obtain existence of solutions to certain classes of stochastic differential equations in the Hermite–Sobolev spaces.

Keywords: Hermite–Sobolev spaces; Tempered distributions; $${\mathcal {S}}^{\prime }$$ S ′ valued processes; Itō formula; Local times; Stochastic integral; Lévy processes; Primary 60H05; Secondary 60H10; 60H15 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-015-0639-3 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:30:y:2017:i:2:d:10.1007_s10959-015-0639-3

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

DOI: 10.1007/s10959-015-0639-3

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 ().