# Regularization of Cylindrical Processes In Locally Convex Spaces

## TL;DR

This paper establishes conditions for the existence of continuous or càdlàg versions of cylindrical processes in the dual of a locally convex space, generalizing prior results and applying to cylindrical Lévy processes.

## Contribution

It introduces new sufficient conditions for the existence of càdlàg or continuous versions of cylindrical processes in duals of locally convex spaces, extending previous literature.

## Key findings

- Provides conditions for càdlàg versions of cylindrical processes
- Generalizes existing results in the literature
- Applies to cylindrical Lévy processes in dual spaces

## Abstract

Let $\Phi$ be a locally convex space and let $\Phi'$ denote its strong dual. In this paper we introduce sufficient conditions for the existence of a continuous or a c\`{a}dl\`{a}g $\Phi'$-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 $\Phi'$-valued c\`{a}dl\`{a}g L\'{e}vy process version to a given cylindrical L\'{e}vy process in $\Phi'$.