Homogenization on nested fractals

T. Kumagai*, S. Kusuoka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


We study the homogenization problem on nested fractals. Let Xt be the continuous time Markov chain on the pre-nested fractal given by putting i.i.d. random resistors on each cell. It is proved that under some conditions, α-nXtnEt converges in law to a constant time change of the Brownian motion on the fractal as n → ∞, where α is the contraction rate and tE 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 martinga e method.

Original languageEnglish
Pages (from-to)375-398
Number of pages24
JournalProbability Theory and Related Fields
Issue number3
Publication statusPublished - 1996 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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