Moment Inequalities for Suprema of Gaussian Random Processes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913848520343552 |
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| author | Diaconu, Simona |
| author_facet | Diaconu, Simona |
| contents | Suppose $(X_t)_{t \in T}$ is a Gaussian process indexed by some arbitrary set $T:$ the random variable $\sup_{t \in T}{X_t}$ can be very intricate and bounding its expectation is a natural step towards understanding it. Sudakov-Fernique inequality allows to order expectations of suprema of such random processes: if $(X_t)_{t \in T},(Y_t)_{t \in T}$ are centered Gaussian random processes satisfying $\mathbb{E}[(X_t-X_s)^2] \leq \mathbb{E}[(Y_t-Y_s)^2]$ for all $t,s \in T,$ then $\mathbb{E}[\sup_{t \in T}{X_t}] \leq \mathbb{E}[\sup_{t \in T}{Y_t}].$ This work obtains similar results for higher moments under a slightly stronger condition than the one aforementioned. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moment Inequalities for Suprema of Gaussian Random Processes Diaconu, Simona Probability Suppose $(X_t)_{t \in T}$ is a Gaussian process indexed by some arbitrary set $T:$ the random variable $\sup_{t \in T}{X_t}$ can be very intricate and bounding its expectation is a natural step towards understanding it. Sudakov-Fernique inequality allows to order expectations of suprema of such random processes: if $(X_t)_{t \in T},(Y_t)_{t \in T}$ are centered Gaussian random processes satisfying $\mathbb{E}[(X_t-X_s)^2] \leq \mathbb{E}[(Y_t-Y_s)^2]$ for all $t,s \in T,$ then $\mathbb{E}[\sup_{t \in T}{X_t}] \leq \mathbb{E}[\sup_{t \in T}{Y_t}].$ This work obtains similar results for higher moments under a slightly stronger condition than the one aforementioned. |
| title | Moment Inequalities for Suprema of Gaussian Random Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2504.12478 |