Upper estimate of martingale dimension for self-similar fractals |
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Authors: | Masanori Hino |
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Institution: | 1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
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Abstract: | We study upper estimates of the martingale dimension d m of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that d m = 1 for natural diffusions on post-critically finite self-similar sets and that d m is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets. |
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