Bounding suprema of canonical processes via convex hull
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916255718440960 |
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| author | Latała, Rafał |
| author_facet | Latała, Rafał |
| contents | We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to date only for a narrow class of regular stochastic processes. We show that for specific index sets, including arbitrary ellipsoids, regularity assumptions may be substantially weakened. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_09463 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounding suprema of canonical processes via convex hull Latała, Rafał Probability 60E15, 60G50, 60G17 We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to date only for a narrow class of regular stochastic processes. We show that for specific index sets, including arbitrary ellipsoids, regularity assumptions may be substantially weakened. |
| title | Bounding suprema of canonical processes via convex hull |
| topic | Probability 60E15, 60G50, 60G17 |
| url | https://arxiv.org/abs/2204.09463 |