Upper estimate of martingale dimension for self-similar fractals
Abstract
We study upper estimates of the martingale dimension dm 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 dm=1 for natural diffusions on post-critically finite self-similar sets and that dm is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.
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