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Brownian motion on a homogeneous random fractal
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  • Published: March 1992

Brownian motion on a homogeneous random fractal

  • B. M. Hambly1 

Probability Theory and Related Fields volume 94, pages 1–38 (1992)Cite this article

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Summary

We introduce a simple random fractal based on the Sierpinski gasket and construct a Brownian motion upon the fractal. The properties of the process on the Sierpinski gasket are modified by the random environment. A sample path construction of the process via time truncation is used, which is a direct construction of the process on the fractal from the associated Dirichlet forms. We obtain estimates on the resolvent and transition density for the process and hence a value for the spectral dimension which satisfiesd s=2d f/dw. A branching process in a random environment can be used to deduce some of the sample path properties of the process.

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Authors and Affiliations

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

    B. M. Hambly

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  1. B. M. Hambly
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Hambly, B.M. Brownian motion on a homogeneous random fractal. Probab. Th. Rel. Fields 94, 1–38 (1992). https://doi.org/10.1007/BF01222507

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  • Received: 04 June 1991

  • Revised: 10 March 1992

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01222507

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Mathematics Subject Classification

  • 60J60
  • 60J25
  • 60J65
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