Local extinction of super-Brownian motion on Sierpiński gasket (Q1128113)

Brownian motion on a Sierpiński gasket (a typical example of a self-similar fractal set of Lebesgue measure zero in two dimensions) was originally studied in detail by \textit{M. T. Barlow} and \textit{E. A. Perkins} [Probab. Theory Relat. Fields 79, No. 4, 543-623 (1988; Zbl 0635.60090)]. A superprocess is a measure-valued stochastic process where the random measure at any time represents the spatial distribution of a population which is both migrating and reproducing. This is called super-Brownian motion on a Sierpiński gasket if the migration component is governed by the process studied by Barlow and Perkins. The present paper addresses two questions: local extinction of the superprocess, and density of the paths of the Brownian motion.