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Pré-Publication, Document De Travail Année : 2024

Fractional stable random fields on the Sierpinski gasket

Résumé

We define and study fractional stable random fields on the Sierpi\'nski gasket. Such fields are formally defined as $(-\Delta)^{-s} W_{K,\alpha}$, where $\Delta$ is the Laplace operator on the gasket and $W_{K,\alpha}$ is a stable random measure. Both Neumann and Dirichlet boundary conditions for $\Delta$ 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.

Dates et versions

hal-04401644 , version 1 (17-01-2024)

Identifiants

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Fabrice Baudoin, Céline Lacaux. Fractional stable random fields on the Sierpinski gasket. 2024. ⟨hal-04401644⟩
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