Noncentral limit results for spatiotemporal random fields on manifolds and beyond

TL;DR

This paper establishes noncentral limit theorems for functionals of certain long-range dependent Gaussian spatiotemporal fields on manifolds and convex sets, using spectral analysis and Wiener chaos techniques.

Contribution

It extends noncentral limit results to LRD Gaussian fields on manifolds and convex sets, employing spectral methods and Wiener chaos reduction.

Findings

Derived NCLTs for Gaussian STRFs on manifolds and convex sets.

Applied spectral analysis to handle pure point and continuous spectra.

Results obtained in the second Wiener Chaos.

Abstract

This paper derives noncentral limit results (NCLTs) for suitable scaling of functionals of spatially homogeneous and isotropic, and stationary in time, LRD Gaussian subordinated Spatiotemporal Random Fields (STRFs) with Hermite rank equal to two. The cases of connected and compact two point homogeneous spaces M_{d} in R^{d+1}, and compact convex sets K in R^{d+1}, whose interior has positive Lebesgue measure, are analyzed. These NCLTs are obtained in the second Wiener Chaos by applying reduction theorems. The methodological approaches adopted in the derivation of these results are based on the pure point and continuous spectra of the Gaussian STRFs subordinators defined on M_{d} and K, respectively.