Asymptotics for isotropic Hilbert-valued spherical random fields
Probability
2022-12-06 v1 Statistics Theory
Statistics Theory
Abstract
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg's theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.
Cite
@article{arxiv.2212.02329,
title = {Asymptotics for isotropic Hilbert-valued spherical random fields},
author = {Alessia Caponera},
journal= {arXiv preprint arXiv:2212.02329},
year = {2022}
}