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Probability Theory and Related Fields

, Volume 79, Issue 4, pp 543–623 | Cite as

Brownian motion on the Sierpinski gasket

  • Martin T. Barlow
  • Edwin A. Perkins
Article

Summary

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).

Keywords

Stochastic Process Brownian Motion Probability Theory Diffusion Process Statistical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

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