Probability Theory and Related Fields

, Volume 91, Issue 3, pp 307–330

Transition densities for Brownian motion on the Sierpinski carpet

Authors

  • Martin T. Barlow
    • Statistical Laboratory
  • Richard F. Bass
    • Department of MathematicsUniversity of Washington
Article

DOI: 10.1007/BF01192060

Cite this article as:
Barlow, M.T. & Bass, R.F. Probab. Th. Rel. Fields (1992) 91: 307. doi:10.1007/BF01192060

Summary

Upper and lower bounds are obtained for the transition densitiesp(t, x, y) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity ofp(t, x, y) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent, is shown to hold.

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© Springer-Verlag 1992