Continuity of Random Fields on Riemannian Manifolds

TL;DR

This paper proves a Kolmogorov--Chentsov type theorem for random fields defined on Riemannian manifolds, extending classical results to a geometric setting.

Contribution

It introduces a new continuity theorem for random fields on Riemannian manifolds, broadening the scope of stochastic process theory.

Findings

Established a Kolmogorov--Chentsov type criterion on manifolds

Extended classical stochastic continuity results to geometric contexts

Provided foundational results for stochastic analysis on manifolds

Abstract

A theorem of the Kolmogorov--Chentsov type is proved for random fields on a Riemannian manifold.