Noncentral limit results for spatiotemporal random fields on manifolds and beyond

This paper derives noncentral limit theorems (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 \mathbb{M}_{d}\subset \mathbb{R}^{d+1}, and compact convex sets \mathcal{K}\subset \mathbb{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 \mathbb{M}_{d} and $\mathcal{K}, respectively.