Shift-invariant homogeneous classes of random fields
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911883859066880 |
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| author | Hashorva, Enkelejd |
| author_facet | Hashorva, Enkelejd |
| contents | Given an $R^d$-valued random field (rf) $Z(t),t\in T$ and an $α$-homogeneous mapping $κ$ we define the corresponding equivalent class of rf's (denoted by $K_α$) which include representers of the same tail measure $ν_Z$. When $T$ is an additive group, tractable equivalent classes of interest are the shift-invariant ones, which contain in particular all independent random shifts of $Z$. This contribution is mainly concerned with the investigation of the probabilistic properties of shift-invariant $K_α$'s. Important objects introduced in our setting are tail and spectral tail rf's. Further, the class of universal maps $U$ acting on elements of $K_α$ turns out to be crucial for properties of functionals of $Z$. Applications of our findings concern max-stable and symmetric $α$-stable rf's, their maximal indices as well as their random shift-representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_00792 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Shift-invariant homogeneous classes of random fields Hashorva, Enkelejd Probability Applications Given an $R^d$-valued random field (rf) $Z(t),t\in T$ and an $α$-homogeneous mapping $κ$ we define the corresponding equivalent class of rf's (denoted by $K_α$) which include representers of the same tail measure $ν_Z$. When $T$ is an additive group, tractable equivalent classes of interest are the shift-invariant ones, which contain in particular all independent random shifts of $Z$. This contribution is mainly concerned with the investigation of the probabilistic properties of shift-invariant $K_α$'s. Important objects introduced in our setting are tail and spectral tail rf's. Further, the class of universal maps $U$ acting on elements of $K_α$ turns out to be crucial for properties of functionals of $Z$. Applications of our findings concern max-stable and symmetric $α$-stable rf's, their maximal indices as well as their random shift-representations. |
| title | Shift-invariant homogeneous classes of random fields |
| topic | Probability Applications |
| url | https://arxiv.org/abs/2111.00792 |