Asymptotics for isotropic Hilbert-valued spherical random fields

Alessia Caponera

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arXiv · 2212.02329

Asymptotics for isotropic Hilbert-valued spherical random fields

Alessia Caponera

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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.

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Alessia Caponera. 2022-12-05. Asymptotics for isotropic Hilbert-valued spherical random fields. https://arxiv.org/abs/2212.02329

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