Factorable continuity of random fields, with quantitative estimation

TL;DR

This paper establishes sufficient conditions for the enhanced continuity of random fields, providing quantitative estimates for the associated random variables and extending the analysis to heavy-tailed distributions and rectangle continuity.

Contribution

It introduces new criteria for factorable continuity of random fields and offers quantitative bounds on the moments of the representing random variables.

Findings

Derived conditions for enhanced continuity of random fields.

Provided estimates for moments of the factorizing random variables.

Extended analysis to heavy-tailed distributions and rectangle continuity.

Abstract

We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of continuity. We estimate also the ordinary and (possible) exponential moments of these random variables. We consider also the case of random fields with heavy tails of distribution and the so-called rectangle its continuity.