Prokhorov-Skorokhod continuity of random fields. A natural approach

TL;DR

This paper establishes natural conditions ensuring the trajectories of certain random fields are in the Prokhorov-Skorokhod space and discusses the Central Limit Theorem within these spaces.

Contribution

It provides sufficient natural conditions for the Prokhorov-Skorokhod continuity of random fields and explores the CLT in these spaces.

Findings

Conditions for Prokhorov-Skorokhod continuity established

Central Limit Theorem proven in these spaces

Trajectories of random fields are shown to belong to the space

Abstract

We derive in this article sufficient conditions in the natural terms for belonging of almost all the trajectories of the certain separable continuous in probability random field to the multivariate Prokhorov-Skorokhod space. We consider also as a consequence the Central Limit Theorem in this spaces.