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Brownian motion on the Sierpinski gasket
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  • Published: November 1988

Brownian motion on the Sierpinski gasket

  • Martin T. Barlow1 &
  • Edwin A. Perkins2 

Probability Theory and Related Fields volume 79, pages 543–623 (1988)Cite this article

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

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Author information

Authors and Affiliations

  1. Statistical Laboratory, 16 Mill Lane, CB2 1SB, Cambridge, UK

    Martin T. Barlow

  2. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, British Columbia, Canada

    Edwin A. Perkins

Authors
  1. Martin T. Barlow
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  2. Edwin A. Perkins
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Additional information

Research partially supported by an NSERC of Canada operating grant

Research partially supported by an SERC (UK) Visiting Fellowship

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Barlow, M.T., Perkins, E.A. Brownian motion on the Sierpinski gasket. Probab. Th. Rel. Fields 79, 543–623 (1988). https://doi.org/10.1007/BF00318785

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  • Received: 20 November 1987

  • Revised: 17 February 1988

  • Issue Date: November 1988

  • DOI: https://doi.org/10.1007/BF00318785

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Diffusion Process
  • Statistical Theory
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