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Homogenization on nested fractals
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  • Published: September 1996

Homogenization on nested fractals

  • T. Kumagai1 &
  • S. Kusuoka2 

Probability Theory and Related Fields volume 104, pages 375–398 (1996)Cite this article

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  • 16 Citations

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Summary

We study the homogenization problem on nested fractals. LetX t be the continuous time Markov chain on the pre-nested fractal given by puttingi.i.d. random resistors on each cell. It is proved that under some conditions,\(\alpha ^{ - n} X_{t_E^n t} \) converges in law to a constant time change of the Brownian motion on the fractal asn→∞, where α is the contraction rate andt E is a time scale constant. As the Brownian motion on fractals is not a semi-martingale, we need a different approach from the well-developed martingale method.

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Author information

Authors and Affiliations

  1. Graduate School of Polymathematics, Nagoya University, Chikusa-ku, 464-01, Nagoya, Japan

    T. Kumagai

  2. Department of Mathematical Sciences, University of Tokyo, 7-3-1 Hongo, Tokyo 113, Japan

    S. Kusuoka

Authors
  1. T. Kumagai
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  2. S. Kusuoka
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Additional information

Dedicated to Professor Masatoshi Fukushima on his 60th birthday

Research partially supported by the Yukawa Foundation

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Cite this article

Kumagai, T., Kusuoka, S. Homogenization on nested fractals. Probab. Th. Rel. Fields 104, 375–398 (1996). https://doi.org/10.1007/BF01213686

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  • Received: 06 April 1995

  • Revised: 11 September 1995

  • Issue Date: September 1996

  • DOI: https://doi.org/10.1007/BF01213686

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Mathematics Subject Classification (1991)

  • 31C25
  • 47A35
  • 60J60
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