%0 Journal Article
%T Upper estimate of martingale dimension for self-similar fractals
%A Masanori Hino
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s00440-012-0442-3
%X 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.
%U http://arxiv.org/abs/1205.5617v2