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A characterization of certain diffusions on the Sierpinski gasket by the exit distributions

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Abstract

LetK be the Sierpinski gasket with verticesa 1,a 2,a 3 forming an equilateral triangle. Suppose that (X t ,P x) and (Y t ,Q x) are diffusions onK with the same hitting probabilities to verticesa 1,a 2,a 3. We show that ifX is an asymptotically one-dimensional diffusion or ap-stream diffusion, thenY is a time-change ofX.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička c. 30, 10000, Zagreb, Croatia

    Zoran Vondraček

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  1. Zoran Vondraček
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Additional information

Part of this work was done while the author was an Alexander von Humboldt fellow at the Universität des Saarlandes in Saarbrücken, Germany.

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Vondraček, Z. A characterization of certain diffusions on the Sierpinski gasket by the exit distributions. J Theor Probab 9, 335–352 (1996). https://doi.org/10.1007/BF02214653

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  • DOI: https://doi.org/10.1007/BF02214653

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