Functional second-order Gaussian Poincaré inequalities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915355758166016 |
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| author | Vidotto, Anna Zheng, Guangqu |
| author_facet | Vidotto, Anna Zheng, Guangqu |
| contents | In this paper, we work in the framework of Hilbert-valued Wiener structures and derive a functional version of the second-order Gaussian Poincaré inequality that leads to abstract bounds for Gaussian process approximation in $d_2$ distance. Our abstract bounds are flexible and can be applied in various examples including functional Breuer-Major central limit theorems, shallow neural networks, and spatial statistics of SPDEs solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional second-order Gaussian Poincaré inequalities Vidotto, Anna Zheng, Guangqu Probability 35Q35, 60F15, 60H30 In this paper, we work in the framework of Hilbert-valued Wiener structures and derive a functional version of the second-order Gaussian Poincaré inequality that leads to abstract bounds for Gaussian process approximation in $d_2$ distance. Our abstract bounds are flexible and can be applied in various examples including functional Breuer-Major central limit theorems, shallow neural networks, and spatial statistics of SPDEs solutions. |
| title | Functional second-order Gaussian Poincaré inequalities |
| topic | Probability 35Q35, 60F15, 60H30 |
| url | https://arxiv.org/abs/2506.13571 |