Dirichlet forms and Brownian motion penetrating fractals
In 1993, \textit{T. Lindstrøm} [Pitman Res. Notes Math. Ser. 283, 148-278 (1993; Zbl 0787.60101)] proved that Brownian motion can penetrate the two-dimensional Sierpinski gasket in the sense that there exists a process which coincides with the ordinary Brownian motion outside the convex hull of the gasket and with the fractal Brownian motion in the gasket. In this paper, the author gives a different proof of this using the theory of Dirichlet forms. The proof of this paper also works in higher dimensions.
scientific article; zbMATH DE number 1523586