Brownian motion on the Sierpinski gasket
We construct a “Brownian motion” taking values in the Sierpinski gasket, a fractal subset of ℝ2, and study its properties. This is a diffusion process characterized by local isotropy and homogeneity properties. We show, for example, that the process has a continuous symmetric transition density, pt(x,y), with respect to an appropriate Hausdorff measure and obtain estimates on pt(x,y).
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