Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space
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 $Φ'$.
math.PR↗