Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds

TL;DR

This paper extends the Kolmogorov-Chentsov theorem to establish sample differentiability and H"older continuity of random fields on manifolds, broadening the theorem's applicability to more complex geometric domains.

Contribution

It generalizes the classical Kolmogorov-Chentsov theorem from domains of cone type to manifolds, providing new theoretical tools for analyzing random fields on complex geometries.

Findings

Proves a version of the Kolmogorov-Chentsov theorem for manifolds.

Establishes conditions for sample differentiability of random fields.

Demonstrates the theorem's applicability to manifold domains.

Abstract

A version of the Kolmogorov-Chentsov theorem on sample differentiability and H\"older continuity of random fields on domains of cone type is proved, and the result is generalized to manifolds.