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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.11198 |
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| _version_ | 1866917213209886720 |
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| author | Weber, Michel |
| author_facet | Weber, Michel |
| contents | We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases.
In the almost periodic case, we prove an approximation theorem. We introduce a modulable diophantine approximation. Finally we study for general non-vanishing coefficient sequences, the behavior along lattices of almost periodic Gaussian polynomials with linearly independent frequencies, and use a lattice localized version of Kronecker's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moderate deviations of suprema of Gaussian processes A cyclic approximation criterion Weber, Michel Probability 42A38, 60G50 We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation theorem. We introduce a modulable diophantine approximation. Finally we study for general non-vanishing coefficient sequences, the behavior along lattices of almost periodic Gaussian polynomials with linearly independent frequencies, and use a lattice localized version of Kronecker's theorem. |
| title | Moderate deviations of suprema of Gaussian processes A cyclic approximation criterion |
| topic | Probability 42A38, 60G50 |
| url | https://arxiv.org/abs/2504.11198 |