Fractional stable random fields on the Sierpiński gasket
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913456828973056 |
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| author | Baudoin, Fabrice Lacaux, Céline |
| author_facet | Baudoin, Fabrice Lacaux, Céline |
| contents | We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as $(-Δ)^{-s} W_{K,α}$, where $Δ$ is the Laplace operator on the gasket and $W_{K,α}$ is a stable random measure. Both Neumann and Dirichlet boundary conditions for $Δ$ are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional stable random fields on the Sierpiński gasket Baudoin, Fabrice Lacaux, Céline Probability We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as $(-Δ)^{-s} W_{K,α}$, where $Δ$ is the Laplace operator on the gasket and $W_{K,α}$ is a stable random measure. Both Neumann and Dirichlet boundary conditions for $Δ$ are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces. |
| title | Fractional stable random fields on the Sierpiński gasket |
| topic | Probability |
| url | https://arxiv.org/abs/2401.08473 |