Necessary and sufficient conditions for continuity of hypercontractive processes and fields

TL;DR

This paper investigates the continuity properties of hypercontractive fields, extending known Gaussian process results to broader classes of processes and fields, with implications for understanding sample path regularity.

Contribution

It provides necessary and sufficient conditions for the continuity of hypercontractive processes and fields, generalizing Gaussian process results beyond Gaussianity.

Findings

Established criteria for continuity of hypercontractive processes

Extended Gaussian continuity results to hypercontractive fields

Applicable to both processes and fields in various dimensions

Abstract

Sample path properties of random processes are an interesting and extensively studied topic, especially in the case of Gaussian processes. In this article, we study the continuity properties of hypercontractive fields, providing natural extensions for some known Gaussian results beyond Gaussianity. Our results apply to both random processes and random fields alike.