Regularization of Cylindrical Processes In Locally Convex Spaces

Abstract

Let $\Phi$ be a locally convex space and let ${\Phi }^{\prime }$ denote its strong dual. In this paper we introduce sufficient conditions for the existence of a continuous or a càdlàg ${\Phi }^{\prime }$-valued version to a cylindrical process defined on $\Phi$. Our result generalizes many other known results on the literature and their different connections will be discussed. As an application, we use our results to show the existence of a ${\Phi }^{\prime }$-valued càdlàg Lévy process version to a given cylindrical Lévy process in ${\Phi }^{\prime }$.

arXiv admin note: text overlap with arXiv:1701.06630, arXiv:1902.03981, arXiv:1806.10231, arXiv:1511.08443