Estimates of transition densities for Brownian motion on nested fractals

Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Citations (Scopus)


We obtain upper and lower bounds for the transition densities of Brownian motion on nested fractals. Compared with the estimate on the Sierpinski gasket, the results require the introduction of a new exponent, dJ, related to the "shortest path metric" and "chemical exponent" on nested fractals. Further, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.

Original languageEnglish
Pages (from-to)205-224
Number of pages20
JournalProbability Theory and Related Fields
Issue number2
Publication statusPublished - 1993 Jun
Externally publishedYes


  • Mathematics Subject Classification: 60J60, 60J65, 60J80

ASJC Scopus subject areas

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


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