Probability Theory and Related Fields

, Volume 96, Issue 2, pp 205–224 | Cite as

Estimates of transition densities for Brownian motion on nested fractals

  • Takashi Kumagai
Article

Summary

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.

Mathematics Subject Classification

60J60 60J65 60J80 

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Takashi Kumagai
    • 1
  1. 1.Department of MathematicsOsaka UniversityOsakaJapan

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