Publication

Asymptotics for Isotropic Hilbert-valued Random Fields

Alessia Caponera
2024

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 highfrequency regime.

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