Spherical Poisson Needlets with Shrinking Bandwidth
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915373939425280 |
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| author | Castaldo, Mattia Durastanti, Claudio |
| author_facet | Castaldo, Mattia Durastanti, Claudio |
| contents | Flexible bandwidth needlets provide a localized multiscale framework with scale-adaptive frequency resolution, enabling effective analysis of spherical Poisson random fields exhibiting spatial inhomogeneity and scale variation. We establish here quantitative Central Limit Theorems for finite-dimensional distributions of spherical Poisson needlets and for the related Poisson needlet coefficients constructed via needlets with shrinking bandwidth on the sphere, and using Stein-Malliavin techniques, we derive explicit rates of normal approximation. In addition, we study the functional convergence of the associated needlet-based random fields. Indeed, our framework provides quantitative control on the limiting behavior in appropriate function spaces. Together, these results offer rigorous probabilistic guarantees for high-resolution spherical data modeling under Poisson sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spherical Poisson Needlets with Shrinking Bandwidth Castaldo, Mattia Durastanti, Claudio Probability 60F05, 60G60 Flexible bandwidth needlets provide a localized multiscale framework with scale-adaptive frequency resolution, enabling effective analysis of spherical Poisson random fields exhibiting spatial inhomogeneity and scale variation. We establish here quantitative Central Limit Theorems for finite-dimensional distributions of spherical Poisson needlets and for the related Poisson needlet coefficients constructed via needlets with shrinking bandwidth on the sphere, and using Stein-Malliavin techniques, we derive explicit rates of normal approximation. In addition, we study the functional convergence of the associated needlet-based random fields. Indeed, our framework provides quantitative control on the limiting behavior in appropriate function spaces. Together, these results offer rigorous probabilistic guarantees for high-resolution spherical data modeling under Poisson sampling. |
| title | Spherical Poisson Needlets with Shrinking Bandwidth |
| topic | Probability 60F05, 60G60 |
| url | https://arxiv.org/abs/2507.05072 |