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Transition probabilities for the simple random walk on the Sierpinski graph

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  • Jones, Owen Dafydd

Abstract

Non-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket.

Suggested Citation

  • Jones, Owen Dafydd, 1996. "Transition probabilities for the simple random walk on the Sierpinski graph," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 45-69, January.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:1:p:45-69
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    Cited by:

    1. Grabner, Peter J. & Woess, Wolfgang, 1997. "Functional iterations and periodic oscillations for simple random walk on the Sierpinski graph," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 127-138, July.
    2. Takashi Kumagai & Chikara Nakamura, 2018. "Lamplighter Random Walks on Fractals," Journal of Theoretical Probability, Springer, vol. 31(1), pages 68-92, March.
    3. Leorato, S. & Orsingher, E., 2009. "Branching on a Sierpinski graph," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 145-154, January.

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