Non-central limit theorems for functionals of random fields on hypersurfaces

TL;DR

This paper establishes non-central limit theorems for nonlinear functionals of Gaussian random fields on hypersurfaces, providing convergence rates and applying results to sojourn measures with various limit behaviors.

Contribution

It extends non-central limit theorems to Gaussian fields on hypersurfaces and derives convergence rates, broadening previous solid figure results.

Findings

Derived non-central limit theorems for hypersurface functionals

Established convergence rates for these functionals

Identified different limit behaviors for sojourn measures

Abstract

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $\mathbb{R}^d$. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.