Brownian motion on the Sierpinski gasket |
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| Authors: | Martin T Barlow Edwin A Perkins |
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| Institution: | (1) Statistical Laboratory, 16 Mill Lane, CB2 1SB Cambridge, UK;(2) Department of Mathematics, University of British Columbia, V6T 1Y4 Vancouver, British Columbia, Canada |
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| Abstract: | Summary We construct a  Brownian motion taking values in the Sierpinski gasket, a fractal subset of  2, 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, p
t(x,y), with respect to an appropriate Hausdorff measure and obtain estimates on p
t(x,y).Research partially supported by an NSERC of Canada operating grantResearch partially supported by an SERC (UK) Visiting Fellowship |
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