Shift-generated $α$-homogeneous classes of jointly measurable random fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909704592031744 |
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| author | Hashorva, Enkelejd |
| author_facet | Hashorva, Enkelejd |
| contents | We consider a class of shift-generated alpha-homogeneous random fields (RFs) C[Z] defined through a functional identity involving a fixed positive alpha and a given jointly measurable R^d-valued RF Z(t),t in R^l. The significance of such classes lies in the fact that their elements generate max-stable and stationary RFs. We extend the original functional identity to a broad class of functionals, including the integral operator S(.) and prove that C[Z] contains at least one L^alpha-continuous element. Finally, we investigate properties of local RFs and their connections with spectral tail and tail RFs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shift-generated $α$-homogeneous classes of jointly measurable random fields Hashorva, Enkelejd Probability Methodology 60G60, 60G70, 60G15 We consider a class of shift-generated alpha-homogeneous random fields (RFs) C[Z] defined through a functional identity involving a fixed positive alpha and a given jointly measurable R^d-valued RF Z(t),t in R^l. The significance of such classes lies in the fact that their elements generate max-stable and stationary RFs. We extend the original functional identity to a broad class of functionals, including the integral operator S(.) and prove that C[Z] contains at least one L^alpha-continuous element. Finally, we investigate properties of local RFs and their connections with spectral tail and tail RFs. |
| title | Shift-generated $α$-homogeneous classes of jointly measurable random fields |
| topic | Probability Methodology 60G60, 60G70, 60G15 |
| url | https://arxiv.org/abs/2507.18835 |