Fractional stable random fields on the Sierpiński gasket

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.