Probability Theory and Related Fields

, Volume 79, Issue 4, pp 543-623

First online:

Brownian motion on the Sierpinski gasket

  • Martin T. BarlowAffiliated withStatistical Laboratory
  • , Edwin A. PerkinsAffiliated withDepartment of Mathematics, University of British Columbia

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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, p t(x,y), with respect to an appropriate Hausdorff measure and obtain estimates on p t(x,y).