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Asymptotically one-dimensional diffusions on the Sierpinski gasket and theabc-gaskets
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  • Published: March 1994

Asymptotically one-dimensional diffusions on the Sierpinski gasket and theabc-gaskets

  • Kumiko Hattori1,
  • Tetsuya Hattori2 &
  • Hiroshi Watanabe3 

Probability Theory and Related Fields volume 100, pages 85–116 (1994)Cite this article

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  • 17 Citations

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Summary

Diffusion processes on the Sierpinski gasket and theabc-gaskets are constructed as limits of random walks. In terms of the associated renormalization group, the present method uses the inverse trajectories which converge to unstable fixed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate fixed points are unnecessary for the construction. A limit theorem related to the discrete-time multi-type non-stationary branching processes is applied.

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Author information

Authors and Affiliations

  1. Department of Pure and Applied Sciences, University of Tokyo, Meguro-ku, 153, Tokyo, Japan

    Kumiko Hattori

  2. Faculty of Engineering, Utsunomiya University, Ishii-cho, 321, Utsunomiya, Japan

    Tetsuya Hattori

  3. Department of Mathematics, Nippon Medical School, Nakahara-ku, 211, Kawasaki, Japan

    Hiroshi Watanabe

Authors
  1. Kumiko Hattori
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  2. Tetsuya Hattori
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  3. Hiroshi Watanabe
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Hattori, K., Hattori, T. & Watanabe, H. Asymptotically one-dimensional diffusions on the Sierpinski gasket and theabc-gaskets. Probab. Th. Rel. Fields 100, 85–116 (1994). https://doi.org/10.1007/BF01204955

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  • Received: 01 March 1993

  • Revised: 25 January 1994

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01204955

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Mathematics Subject Classification

  • 60J60
  • 60J25
  • 60J85
  • 60J15
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