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 Upper estimate of martingale dimension for self-similar fractals


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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.



Author: Masanori Hino

Source: https://archive.org/







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