Asymptotics for isotropic Hilbert-valued spherical random fields. (English) Zbl 07874398
Summary: 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.
MSC:
| 60G60 | Random fields |
| 60F05 | Central limit and other weak theorems |
| 62M15 | Inference from stochastic processes and spectral analysis |
Keywords:
high-frequency asymptotics; Hilbert spaces; isotropy; quantitative central limit theorem; spectral representation; spherical random fieldsReferences:
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