Summary
Diffusion processes on the Sierpinski gasket and theabc-gaskets are constructed as limits of random walks. In terms of the associated renormalization group, the present method uses the inverse trajectories which converge to unstable fixed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate fixed points are unnecessary for the construction. A limit theorem related to the discrete-time multi-type non-stationary branching processes is applied.
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Hattori, K., Hattori, T. & Watanabe, H. Asymptotically one-dimensional diffusions on the Sierpinski gasket and theabc-gaskets. Probab. Th. Rel. Fields 100, 85–116 (1994). https://doi.org/10.1007/BF01204955
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DOI: https://doi.org/10.1007/BF01204955
Mathematics Subject Classification
- 60J60
- 60J25
- 60J85
- 60J15