Regularization of cylindrical processes in locally convex Spaces

Abstract

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