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

2015/11/26 by Christian Fonseca-Mora · 1 citation
Mathematics · #math.PR

paper · pdf · doi:10.1007/s10959-016-0726-0

published as J Theor Probab, 31, no.2, 867-894 (2018)

arxiv created 2015/11/26 · arxiv updated 2018/06/25

Abstract

Let Φ be a nuclear space and let Φ'_β denote its strong dual. In this paper we introduce sufficient conditions for a cylindrical process in Φ' to have a version that is a Φ'_β-valued continuous or cádlág 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 Φ'_β. Finally, we apply our results to the study of properties of cylindrical martingales in Φ'.

Cited by

• Regularization of Cylindrical Processes In Locally Convex Spaces
• Itô's formula for Lévy-Itô processes taking values in the dual of nuclear space