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Estimates of transition densities for Brownian motion on nested fractals
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  • Published: June 1993

Estimates of transition densities for Brownian motion on nested fractals

  • Takashi Kumagai1 

Probability Theory and Related Fields volume 96, pages 205–224 (1993)Cite this 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,d J, 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.

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Authors and Affiliations

  1. Department of Mathematics, Osaka University, Toyonaka, 560, Osaka, Japan

    Takashi Kumagai

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  1. Takashi Kumagai
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Kumagai, T. Estimates of transition densities for Brownian motion on nested fractals. Probab. Th. Rel. Fields 96, 205–224 (1993). https://doi.org/10.1007/BF01192133

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  • Received: 10 October 1991

  • Revised: 15 January 1993

  • Issue Date: June 1993

  • DOI: https://doi.org/10.1007/BF01192133

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Mathematics Subject Classification

  • 60J60
  • 60J65
  • 60J80
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