Probability Theory and Related Fields

, Volume 79, Issue 4, pp 543–623

Brownian motion on the Sierpinski gasket

  • Martin T. Barlow
  • Edwin A. Perkins

DOI: 10.1007/BF00318785

Cite this article as:
Barlow, M.T. & Perkins, E.A. Probab. Th. Rel. Fields (1988) 79: 543. doi:10.1007/BF00318785


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).

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Martin T. Barlow
    • 1
  • Edwin A. Perkins
    • 2
  1. 1.Statistical LaboratoryCambridgeUK
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada