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arXiv · 1511.08443

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

Christian Fonseca-Mora
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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 $Φ'$.

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Christian Fonseca-Mora. 2015-11-26. Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space. https://doi.org/10.1007/s10959-016-0726-0

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