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Fractional stable random fields on the Sierpiński gasket

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  • Baudoin, Fabrice
  • Lacaux, Céline

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.

Suggested Citation

  • Baudoin, Fabrice & Lacaux, Céline, 2024. "Fractional stable random fields on the Sierpiński gasket," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s030441492400187x
    DOI: 10.1016/j.spa.2024.104481
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    References listed on IDEAS

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    6. Baudoin, Fabrice & Chen, Li, 2023. "Dirichlet fractional Gaussian fields on the Sierpinski gasket and their discrete graph approximations," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 593-616.
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