Fractional stable random fields on the Sierpiński gasket

Fabrice Baudoin and Céline Lacaux

Stochastic Processes and their Applications, 2024, vol. 178, issue C

Abstract: We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as (−Δ)−sWK,α, where Δ is the Laplace operator on the gasket and WK,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.

Keywords: Fractional stable fields; Fractional Riesz kernels; Hölder continuity (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104481

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