Fractional stable random fields on the Sierpi\'nski gasket

Abstract

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.