Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space

C. A. Fonseca-Mora ()
Additional contact information
C. A. Fonseca-Mora: Universidad de Costa Rica

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 867-894

Abstract: Abstract Let $$\Phi $$ Φ be a nuclear space and let $$\Phi '_{\beta }$$ Φ β ′ denote its strong dual. In this paper, we introduce sufficient conditions for a cylindrical process in $$\Phi '$$ Φ ′ to have a version that is a $$\Phi '_{\beta }$$ Φ β ′ -valued continuous or càdlàg process. We also establish sufficient conditions for the existence of such a version taking values and having finite moments in a Hilbert space continuously embedded in $$\Phi '_{\beta }$$ Φ β ′ . Finally, we apply our results to the study of properties of cylindrical martingales in $$\Phi '$$ Φ ′ .

Keywords: Cylindrical stochastic processes; Dual of a nuclear space; Continuous and càdlàg versions; Cylindrical martingales; 60B11; 60G20; 60G17; 28C20 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-016-0726-0 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:31:y:2018:i:2:d:10.1007_s10959-016-0726-0

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

DOI: 10.1007/s10959-016-0726-0

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 ().